河川径流时间序列的非线性特征识别与分析
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摘要
对径流变化规律的研究是水资源合理开发利用,流域规划管理的前提和基础。由于径流是一个连续的过程,而径流序列却是一种复杂的离散的非线性数据,径流数据噪声、数据误差等大量的随机因素影响径流序列的建模和预测。过去的几十年,人们一直用基于相空间重构的常用方法来描述径流演变过程,揭示径流演变的规律。本文基于以前研究的研究方法和理论成果,引入0-1混沌测试二元方法、递归图分析理论、顺模式递归图理论和复杂网络理论,与混沌理论相结合,应用于河川径流演变规律的研究中。并以长江流域多个水文站和美国Oregon州的Umpqua河Elkton站统计的多年日径流资料为研究对象,对径流时间序列混沌特征的时间和空间尺度问题进行了定性的描述和定量的分析,主要研究成果如下；
1.本文提出了一种新的时间序列混沌特性识别方法：0-1混沌测试方法。该方法直接应用于时间序列而不需要相空间重构,并且通过量化指标Kc是否接近于0或1来识别时间序列的混沌特性。以Logistic映射生成的序列、金沙江流域和美国Umpqua河多年日径流序列为研究对象,利用0-1混沌测试方法进行了混沌特性识别和判定；与传统的基于相空间重构的关联维数方法、最大Lyapunov指数法和Kolmogorov熵方法进行对比分析,结果表明这两列径流时间序列存在低维混沌特性,并验证了该方法是径流时间序列分析的一种简单、有效和可靠的工具。
2.一般认为径流序列的动力行为是复杂的非线性和多尺度现象的综合作用的外在表现。基于混沌理论和相空间重构理论,本文以金沙江和美国Umpqua可统计的日径流序列为研究对象,对不同时间尺度(日,旬和月)的径流序列,首先利用0-1混沌测试算法计算其渐进增长率Kc,探讨径流序列混沌特性随时间尺度的变化规律；然后重构以上径流序列的相空间,分别计算关联维数、最大Lyapunov旨数和Kolmogorov熵。用这三个混沌判别指标分析不同时间尺度下径流序列的混沌特性及其随时间尺度的变化规律。研究结果表明,时间尺度和径流序列非线性特征之间的关系还不明显,渐进增长率随时间尺度的增加并无明显的变化规律,嵌入维数则随时间尺度的增大呈减小趋势,最大lyapunov指数和Kolmogorov熵随着时间尺度的增加逐渐增大。
3.本文提出基于相空间重构理论的递归图和顺模式递归图理论来获取水文时间序列的动力学行为的新方法。在计算随机、正弦(?)Logistic映射3种典型时间序列的递归图的基础上,采用递归图分析获取不同时间尺度的径流时间序列的动力学行为的方法,通过波动模式的分析和确定性识别,定性地判断径流序列所具有的确定性和不确定性成分。同时,采用递归定量分析方法(RQA),刻画了不同时间尺度的径流序列的复杂度,通过对不同时间尺度径流序列的递归图和递归定量参数的对比,分析了径流序列随时间尺度的变化规律,验证了递归定量分析和顺模式递归定量分析是一种识别非线性时间序列的有效的工具。
4.介绍了一种基于相空间重构的复杂网络构造方法,并将之应用于水文时间序列分析领域,为水文时间序列分析提供了新的视角。一个周期的时间序列可以通过网络化方法转化为周期的复杂网络,随机的时间序列构建成具有随机特性的复杂网络,混沌的时间序列构建出具有小世界效应和无标度特性的的复杂网络。随后对长江流域不同水文站统计的日径流序列进行复杂网络构建,并利用提出的基于K-means聚类社团探寻社团算法对构造的复杂网络进行社团划分,讨论了径流时间序列的复杂网络性特征。并从模块化、社团数、平均路径长度,图密度、平均聚类系数,平均度值与度分布、平均社团重叠度和平均嵌入等网络量化指标反映径流序列的空间尺度的网络特性,从网络化的视角定性和定量的探索径流序列复杂网络节点波动模式特征随流域面积的变化规律,对于径流序列的建模和预测具有一定的参考价值。
The study of the regularity for the daily runoff time series is the prerequisite and foundation in hydrochemistry and development using of water resource, modeling towards planning and management of river basins. Hydrological process is a suquence course; however, runoff series is a complex, discrete and nonlinear data. A large number of random factors, such as data noise and the length of data, would have an effect on the mathematic model establish and predictions. For a long time, people analyse and study runoff fluctuation frequency and evolution process using the traditional method based on the phase-space reconstruction. Based on the previse research methods and theoretical results, some newly nonlinear time series theory and analyzes methods:the zero-one (0-1) test algorithm, recurrence plot and recurrence quantification analysis (RQA) theory, and complex network reconstruction theory, is put forward in which the chaos theory is combined to compute, discuss and slove on the river runoff. Case studies of daily discharges of Yangtze River (Hankou station, Yichang station and Pingshan station) in china and Umpqua River in America (Elkton station) are implemented. The main research contents and research achievement of this paper are as follows:
1. This paper presents a new effective algorithm for chaos detection in time series named0-1test fo chaos. The advantages of the method is that it can applies directly to time series data and phase space reconstruction is not necessary. Moreover, the non-chaotic and chaotic characteristic can be decided by means of the parameters Kc approaching asymptotically either to zero or one. Case studies of Logistic map, daily runoff series of Jinsha River in China and Umpqua River in America are implemented. The chaotic characteristics are identified and verified by using the0-1test algorithm. Then, based on the phase space reconstruction, nonlinear dynamic methods are employed, for example correlation dimension method, Lyapunov exponent method and Kolmogorov entropy. The comparison results show the effectiveness and reliability of the0-1test algorithm. The results from these methods provide cross-verification and confirmation of the existence of a mild low-dimensional chaos in the two daily runoff time series.
2. Natural runoff dynamics is an outcome of complex nonlinear and multi-scale phenomena, integrated together in some coherent manner. Based on chaos theory and the phase space reconstruction theory, daily runoff series of Jinsha River in china and Umpqua River in America are used for this study at different timescales (one day,1/3month and one month). This paper calculates the asymptotic growth rate Kc by the0-1test algorithm and its variation with timescales are explored firstly. Then phase space reconstruction are adopted for the runoff series, three discrimination indexes, correlation dimension, Lyapunov exponent and Kolmogorov entropy, are used:An attempt is made to identify the existence of chaos and the intensity of nonlinear behavior at three characteristic time scales. A comparison of results reveals the relationship of the timescales and the intensity of nonlinearity is not very obvious, no clear variation is found between the asymptotic growth rate and the timescale, the embedded dimension decrease as the timescales increase. However, largest Lyapunov exponent and Kolmogorov entropy increases with the increase of the timescale.
3. The method of recurrence plot and order pattant recurrence plot are proposed to get dynamic characteristics property of hydrological time series, which is based on reconstruction phase space. After structuring recurrence plots for Brownian movement, the Lorenz system and periodic sequence (Logisticc map and sine function), the recurrence plots of daily runoff time series at different timescale were studied quantitatively. Through the analysis of fluctuation patterns and identification of deterninacy, the certainty and uncertainty components were identified in the runoff time series. Then, the Recurrence quantification analysis (RQA) is used for characterizing complexity analysis of runoff series, the recurrence plot and recurrence parameters of five different runoff series are compared. The results show the analysis method is a valid effective means for ranoff fluctuation pattern and evolution rule.
4. This paper introduced a new method for model of complex networks based on renormalization from a time series-Complex Network based on Phase Space. It is used in hydrology and water resources research, the method has offered an interesting new angle on analyses of the hydrological time series. Prior studies on the statistical properties of network topotogy, shows that the constructed complex network model contained inherent characteristics of the time series in its structure. Specifically, a set of periodic data and noisy series could be transformed into a deteminate networks and stochastic networks, respectively, and the chaotic complex networks typically show the properties of small-world and scale-free property involved in unstable periodic trajectories. Then the study focused on the construction of complex network of dialy runoff seires in Yangtze River at different hydrological station. The complex network characteristic of the runoff time series is discussed. Then the community-detection algorithm based on K-means clustering is proposed and detecting the community structure of the complex network of runoff time series. We investigate the correspondence between the dynamics of runoff time series and the node fluctuation patterns distribution of complex network. And the characteristics of different space scale diarly runoff series are depicted by the network parameters, including average degree, graph density, modularity, number of communities, average clustering coefficient, and average path lengh, number of shortest paths, average neighborhood overlap and average embeddness. This is a great reference value of modeling and prediction of runoff series from the prospective of network.
1.本文提出了一种新的时间序列混沌特性识别方法：0-1混沌测试方法。该方法直接应用于时间序列而不需要相空间重构,并且通过量化指标Kc是否接近于0或1来识别时间序列的混沌特性。以Logistic映射生成的序列、金沙江流域和美国Umpqua河多年日径流序列为研究对象,利用0-1混沌测试方法进行了混沌特性识别和判定；与传统的基于相空间重构的关联维数方法、最大Lyapunov指数法和Kolmogorov熵方法进行对比分析,结果表明这两列径流时间序列存在低维混沌特性,并验证了该方法是径流时间序列分析的一种简单、有效和可靠的工具。
2.一般认为径流序列的动力行为是复杂的非线性和多尺度现象的综合作用的外在表现。基于混沌理论和相空间重构理论,本文以金沙江和美国Umpqua可统计的日径流序列为研究对象,对不同时间尺度(日,旬和月)的径流序列,首先利用0-1混沌测试算法计算其渐进增长率Kc,探讨径流序列混沌特性随时间尺度的变化规律；然后重构以上径流序列的相空间,分别计算关联维数、最大Lyapunov旨数和Kolmogorov熵。用这三个混沌判别指标分析不同时间尺度下径流序列的混沌特性及其随时间尺度的变化规律。研究结果表明,时间尺度和径流序列非线性特征之间的关系还不明显,渐进增长率随时间尺度的增加并无明显的变化规律,嵌入维数则随时间尺度的增大呈减小趋势,最大lyapunov指数和Kolmogorov熵随着时间尺度的增加逐渐增大。
3.本文提出基于相空间重构理论的递归图和顺模式递归图理论来获取水文时间序列的动力学行为的新方法。在计算随机、正弦(?)Logistic映射3种典型时间序列的递归图的基础上,采用递归图分析获取不同时间尺度的径流时间序列的动力学行为的方法,通过波动模式的分析和确定性识别,定性地判断径流序列所具有的确定性和不确定性成分。同时,采用递归定量分析方法(RQA),刻画了不同时间尺度的径流序列的复杂度,通过对不同时间尺度径流序列的递归图和递归定量参数的对比,分析了径流序列随时间尺度的变化规律,验证了递归定量分析和顺模式递归定量分析是一种识别非线性时间序列的有效的工具。
4.介绍了一种基于相空间重构的复杂网络构造方法,并将之应用于水文时间序列分析领域,为水文时间序列分析提供了新的视角。一个周期的时间序列可以通过网络化方法转化为周期的复杂网络,随机的时间序列构建成具有随机特性的复杂网络,混沌的时间序列构建出具有小世界效应和无标度特性的的复杂网络。随后对长江流域不同水文站统计的日径流序列进行复杂网络构建,并利用提出的基于K-means聚类社团探寻社团算法对构造的复杂网络进行社团划分,讨论了径流时间序列的复杂网络性特征。并从模块化、社团数、平均路径长度,图密度、平均聚类系数,平均度值与度分布、平均社团重叠度和平均嵌入等网络量化指标反映径流序列的空间尺度的网络特性,从网络化的视角定性和定量的探索径流序列复杂网络节点波动模式特征随流域面积的变化规律,对于径流序列的建模和预测具有一定的参考价值。
The study of the regularity for the daily runoff time series is the prerequisite and foundation in hydrochemistry and development using of water resource, modeling towards planning and management of river basins. Hydrological process is a suquence course; however, runoff series is a complex, discrete and nonlinear data. A large number of random factors, such as data noise and the length of data, would have an effect on the mathematic model establish and predictions. For a long time, people analyse and study runoff fluctuation frequency and evolution process using the traditional method based on the phase-space reconstruction. Based on the previse research methods and theoretical results, some newly nonlinear time series theory and analyzes methods:the zero-one (0-1) test algorithm, recurrence plot and recurrence quantification analysis (RQA) theory, and complex network reconstruction theory, is put forward in which the chaos theory is combined to compute, discuss and slove on the river runoff. Case studies of daily discharges of Yangtze River (Hankou station, Yichang station and Pingshan station) in china and Umpqua River in America (Elkton station) are implemented. The main research contents and research achievement of this paper are as follows:
1. This paper presents a new effective algorithm for chaos detection in time series named0-1test fo chaos. The advantages of the method is that it can applies directly to time series data and phase space reconstruction is not necessary. Moreover, the non-chaotic and chaotic characteristic can be decided by means of the parameters Kc approaching asymptotically either to zero or one. Case studies of Logistic map, daily runoff series of Jinsha River in China and Umpqua River in America are implemented. The chaotic characteristics are identified and verified by using the0-1test algorithm. Then, based on the phase space reconstruction, nonlinear dynamic methods are employed, for example correlation dimension method, Lyapunov exponent method and Kolmogorov entropy. The comparison results show the effectiveness and reliability of the0-1test algorithm. The results from these methods provide cross-verification and confirmation of the existence of a mild low-dimensional chaos in the two daily runoff time series.
2. Natural runoff dynamics is an outcome of complex nonlinear and multi-scale phenomena, integrated together in some coherent manner. Based on chaos theory and the phase space reconstruction theory, daily runoff series of Jinsha River in china and Umpqua River in America are used for this study at different timescales (one day,1/3month and one month). This paper calculates the asymptotic growth rate Kc by the0-1test algorithm and its variation with timescales are explored firstly. Then phase space reconstruction are adopted for the runoff series, three discrimination indexes, correlation dimension, Lyapunov exponent and Kolmogorov entropy, are used:An attempt is made to identify the existence of chaos and the intensity of nonlinear behavior at three characteristic time scales. A comparison of results reveals the relationship of the timescales and the intensity of nonlinearity is not very obvious, no clear variation is found between the asymptotic growth rate and the timescale, the embedded dimension decrease as the timescales increase. However, largest Lyapunov exponent and Kolmogorov entropy increases with the increase of the timescale.
3. The method of recurrence plot and order pattant recurrence plot are proposed to get dynamic characteristics property of hydrological time series, which is based on reconstruction phase space. After structuring recurrence plots for Brownian movement, the Lorenz system and periodic sequence (Logisticc map and sine function), the recurrence plots of daily runoff time series at different timescale were studied quantitatively. Through the analysis of fluctuation patterns and identification of deterninacy, the certainty and uncertainty components were identified in the runoff time series. Then, the Recurrence quantification analysis (RQA) is used for characterizing complexity analysis of runoff series, the recurrence plot and recurrence parameters of five different runoff series are compared. The results show the analysis method is a valid effective means for ranoff fluctuation pattern and evolution rule.
4. This paper introduced a new method for model of complex networks based on renormalization from a time series-Complex Network based on Phase Space. It is used in hydrology and water resources research, the method has offered an interesting new angle on analyses of the hydrological time series. Prior studies on the statistical properties of network topotogy, shows that the constructed complex network model contained inherent characteristics of the time series in its structure. Specifically, a set of periodic data and noisy series could be transformed into a deteminate networks and stochastic networks, respectively, and the chaotic complex networks typically show the properties of small-world and scale-free property involved in unstable periodic trajectories. Then the study focused on the construction of complex network of dialy runoff seires in Yangtze River at different hydrological station. The complex network characteristic of the runoff time series is discussed. Then the community-detection algorithm based on K-means clustering is proposed and detecting the community structure of the complex network of runoff time series. We investigate the correspondence between the dynamics of runoff time series and the node fluctuation patterns distribution of complex network. And the characteristics of different space scale diarly runoff series are depicted by the network parameters, including average degree, graph density, modularity, number of communities, average clustering coefficient, and average path lengh, number of shortest paths, average neighborhood overlap and average embeddness. This is a great reference value of modeling and prediction of runoff series from the prospective of network.
引文
[1]李士勇,田新华.非线性科学与复杂性科学[M].哈尔滨工业大学出版社,2006.
[2]王兴元.复杂非线性系统中的混沌[M].电子工业出版社,2003.
[3]陈关荣,吕金虎.Lorenz系统族的动力学分析,控制与同步[M].科学出版社,2003.
[4]张济世,刘立昱,程中山.统计水文学[M].黄河水利出版社,2006.
[5]李彦彬.河川径流的混沌特征和预测研究[D].西安理工大学,2009.
[6]洛伦兹EN.混沌的本质[J].北京：气象出版版社,1997：152-159.
[7]刘建香.复杂网络及其在国内研究进展的综述[J].系统科学学报,2009(4).
[8]陶瑾,陈晓红,汪丽娜,谢毅文.北江流域径流时间序列的分形特征解析[J].中山大学学报,2011,50(5)：148-152.
[9]魏茹.多元混沌时间序列的变量选择及预测方法研究[D].大连理工大学,2007.
[10]佟春生.复杂性理论在河川径流时间序列分析中的应用研究[D].西安理工大学,2005.
[11]米红,张文璋.实用现代统计分析方法与SPSS应用[J].北京：当代中国出版社,2000,10.
[12]刘洪,李必强.基于混沌吸引子的时间序列预测[J].系统工程与电子技术,1997,19(2)：23-28.
[13]韩敏.混沌时间序列预测理论与方法[M].中国水利水电出版社,2007.
[14]黄国如,芮孝芳.流域降雨径流时间序列的混沌识别及其预测研究进展[J].水科学进展,2004,15(2)：255-260.
[15]Rodriguez-Iturbe I, Febres De Power B, Sharifi M B, et al. Chaos in rainfall [J]. Water Resources Research,1989,25(7):1667-1675.
[16]夏荣尧.基于ARIMA模型的我国通货膨胀预测研究[D].湖南大学,2009.
[17]Wilcox B P, Seyfried M S, Matison T H. Searching for chaotic dynamics in snowmelt runoff [J]. Water Resources Research,1991,27(6):1005-1010.
[18]Jayawardena A W, Lai F. Analysis and prediction of chaos in rainfall and stream flow time series [J]. Journal of Hydrology,1994,153(1):23-52.
[19]Sivakumar B, Liong S Y, Liaw C Y. EVIDENCE OF CHAOTIC BEHAVIOR IN SINGAPORE RAINFALL1 [J]. JAWRA Journal of the American Water Resources Association,1998,34(2):301-310.
[20]Sivakumar B, Phoon K K, Liong S Y, et al. A systematic approach to noise reduction in chaotic hydrological time series [J]. Journal of hydrology,1999,219(3):103-135.
[21]Sivakumar B, Berndtsson R, Olsson J, et al. Evidence of chaos in the rainfall-runoff process [J]. Hydrological Sciences Journal,2001,46(1):131-145.
[22]Sivakumar B, Sorooshian S, Gupta H V, et al. A chaotic approach to rainfall disaggregation [J]. Water Resources Research,2001,37(1):61-72.
[23]Sivakumar B. Chaos in rainfall:variability, temporal scale and zeros [J]. Journal of Hydroinformatics,2005,7:175-184.
[24]Wang W, Vrijling J K, Van Gelder P H, et al. Testing for nonlinearity of streamflow processes at different timescales [J]. Journal of Hydrology,2006,322(1):247-268.
[25]Ng W W, Panu U S, Lennox W C. Chaos based analytical techniques for daily extreme hydrological observations [J]. Journal of Hydrology,2007,342(1):17-41.
[26]Zhang L, Xia J, Song X, et al. Similarity model of chaos phase space and its application in mid-and long-term hydrologic prediction [J]. Kybernetes,2009,38(10): 1835-1842.
[27]Ghorbani M A, Kisi O, Aalinezhad M. A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods [J]. Applied Mathematical Modelling,2010,34(12):4050-4057.
[28]Dhanya C T, Nagesh Kumar D. Nonlinear ensemble prediction of chaotic daily rainfall [J]. Advances in Water Resources,2010,33(3):327-347.
[29]Dhanya C T, Nagesh Kumar D. Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs [J]. Journal of Hydrology,2011,403(3):292-306.
[30]Khatibi R, Sivakumar B, Ghorbani M A, et al. Investigating chaos in river stage and discharge time series [J]. Journal of Hydrology,2012,414:108-117.
[31]丁晶,邓育仁,吴伯贤.洪水混沌分析[J].水资源研究,1992,13(3)：14-18.
[32]王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析[J].水科学进展,1994,5(2)：87-94.
[33]傅军,丁晶,邓育仁.洪水混沌特性初步研究[J].水科学进展,1996,7(3)：226-230.
[34]赵永龙,丁晶,邓育仁.相空间小波网络模型及其在水文中长期预测中的应用[J].水科学进展,1999,9(3)：252-257.
[35]温权,张士军,张周胜.探求径流序列中的混沌特征[J].水电能源科学,1999,17(1)：21-23.
[36]赵永龙,常晓青,丁晶,邓育仁.水文动力系统重建相空间嵌入维数研究[J].人民长江,1999,30：43-45.
[37]陈云浩,史培军,李晓兵.不同热力背景对城市降雨(暴雨)的影响(Ⅱ)-降雨时序的混沌分析[J].2001,10(3)：20-25.
[38]袁鹏,李谓新,王文圣,丁晶.月降雨量时间序列中的混沌现象[J].四川大学学报(工程科学报),2002,34(1)16-19.
[39]李眉眉,丁晶,王文圣.基于混沌理论的径流降尺度分析[J].四川大学学报(工程科学版),2004,3：003.
[40]李荣峰,沈冰,张金凯.基于相空间重构的水文自记忆预测模型[J].水利学报,2006,5：583-591.
[41]于国荣,夏自强.混沌时间序列支持向量机模型及其在径流预测中应用[J].水科学进展,2008,19(1)：116-122.
[42]Porporato A, Ridolfi L. Clues to the existence of deterministic chaos in river flow [J]. International Journal of modern physics B,1996,10(15):1821-1862.
[43]Sivakumar B. Correlation dimension estimation of hydrological series and data size requirement:myth and reality/Estimation de la dimension de correlation de series hydrologiques et taille necessaire du jeu de donnees:mythe et realite [J]. Hydrological sciences journal,2005,50(4).
[44]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择[J].系统仿真学报,2007,19(11)：2527-2530.
[45]徐自励,王一扬,周激流.估计非线性时间序列嵌入延迟时间和延迟时间窗的C-C平均方法[J].四川大学学报(工程科学版),2007,39(1)：151-155.
[46]Osborne A R, Provenzale A. Finite correlation dimension for stochastic systems with power-law spectra [J]. Physica D:Nonlinear Phenomena,1989,35(3):357-381.
[47]Rapp P E, Albano A M, Schmah T I, et al. Filtered noise can mimic low-dimensional chaotic attractors [J]. Physical review E,1993,47(4):2289.
[48]Provenzale A, Osborne A R, Soj R. Convergence of the K2 entropy for random noises with power law spectra [J]. Physica D:Nonlinear Phenomena,1991,47(3):361-372.
[49]Gottwald G A, Melbourne I. On the implementation of the 0-1 test for chaos [J]. SIAM Journal on Applied Dynamical Systems,2009,8(1):129-145.
[50]Skokos C, Antonopoulos C, Bountis T C, et al. Detecting order and chaos in Hamiltonian systems by the SALI method [J]. Journal of Physics A:Mathematical and General,2004,37(24):6269.
[51]Martinsen-Burrell N, Julien K, Petersen M R, et al. Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices [J]. Physics of Fluids,2006,18:057101.
[52]Gottwald G A, Melbourne I. Testing for chaos in deterministic systems with noise [J]. Physica D:Nonlinear Phenomena,2005,212(1):100-110.
[53]Falconer I, Gottwald G A, Melbourne I, et al. Application of the 0-1 test for chaos to experimental data [J]. SIAM Journal on Applied Dynamical Systems,2007,6(2): 395-402.
[54]Eckmann J P, Kamphorst S O, Ruelle D. Recurrence plots of dynamical systems [J]. EPL (Europhysics Letters),1987,4(9):973.
[55]Trulla L L, Giuliani A, Zbilut J P, et al. Recurrence quantification analysis of the logistic equation with transients [J]. Physics Letters A,1996,223(4):255-260.
[56]Yang Y, Yang H. Complex network-based time series analysis [J]. Physica A: Statistical Mechanics and its Applications,2008,387(5):1381-1386.
[57]汪小帆,刘亚冰.复杂网络中的社团结构算法综述[J].电子科技大学学报,2009,38(5)：537-543.
[58]郝柏林.复杂性的刻画与复杂性科学[J].科学,1999,51(3)：3-8.
[59]李国良.混沌理论及其在水文时间序列中的应用[D].东北农业大学,2007.
[60]Li T Y, Yorke J A. Period three implies chaos [J]. The American Mathematical Monthly,1975,82(10):985-992.
[61]Devaney R L. An introduction to chaotic dynamical systems [J].2003.
[62]李健.动力系统的复杂性及其应用[D].中国科学技术大学,2012.
[63]唐强.基于复杂网络理论的径流时间序列非线性性质研究[D].武汉大学,2011.
[64]张丽娟.离散动力系统的混沌判定和扰动[D].山东大学,2011
[65]郑金.短期电力负荷预测方法研究[D].2012.
[66]Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length [J]. Physica D:Nonlinear Phenomena, 1996,95(1):13-28.
[67]王抵修.地学数据分析中的相空间重构预测方法研究[D].吉林大学,2008.
[68]Takens F. Detecting strange attractors in turbulence [M]. Dynamical systems and turbulence, Warwick 1980. Springer Berlin Heidelberg,1981:366-381.
[69]甘建超.混沌信号处理在雷达和通信对抗中的应用[D].电子科技大学,2004
[70]刘力.三峡流域径流特性分析及预测研究[D].华中科技大学,2009.
[71]Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times, and embedding windows [J]. Physica D:Nonlinear Phenomena,1999,127(1):48-60.
[72]刘文博.混沌时间序列分析与计算方法及应用研究[D].大连理工大学,2008
[73]杨世锡.柯尔莫哥洛夫嫡及其在故障诊断中的应用[J].机械科学与技术,2000, 19(1)：6-8.
[74]Kennel M B, Brown R, Abarbanel H D I. Determining embedding dimension for phase-space reconstruction using a geometrical construction [J]. Physical review A, 1992,45(6):3403.
[75]许小可.基于非线性分析的海杂波处理与目标检测[D].大连海事大学,2008.
[76]Cao L. Practical method for determining the minimum embedding dimension of a scalar time series [J]. Physica D:Nonlinear Phenomena,1997,110(1):43-50.
[77]Grassberger P, Procaccia I. Characterization of strange attractors[J]. Physical review letters,1983,50(5):346-349.
[78]于青.关联维数计算的分析研究[J].天津理工学院学报,2004,20(4)：60-62.
[79]Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series[J]. Physica D:Nonlinear Phenomena,1985,16(3):285-317.
[80]Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets [J]. Physica D:Nonlinear Phenomena,1993, 65(1):117-134.
[81]余波,李应红,张朴.关联维数和Kofmognrov嫡在航空发动机故障诊断中的应用[J].航空动力学报,2006.2
[82]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究[J].计算机工程与应用,2006,21：162-164.
[83]王蕾.基于互信息网络模型的冰雹回波时间序列知识发现[D].天津大学,2008.
[84]李新杰,胡铁松,郭旭宁,等.0—1测试方法的径流时间序列混沌特性应用[J].水科学进展,2012,23(6)：861-868.
[85]王云琦,齐实,孙阁,等.气候与土地利用变化对流域水资源的影响：以美国北卡罗莱纳州Trent流域为例[J].水科学进展,2011,22(1)：51-58.
[86]涂新军,陈晓宏,张强,等.东江径流年内分配特征及影响因素贡献分解[J].水科学进展,2012,23(4)：465-474.
[87]Ghorbani M A, Kisi O, Aalinezhad M. A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods [J]. Applied Mathematical Modelling,2010,34(12):4050-4057.
[88]Ke-Hui S, Xuan L, Cong-Xu Z. The 0-1 test algorithm for chaos and its applications [J]. Chinese Physics B,2010,19(11):110510.
[89]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2)：55-58.
[90]Zhao H, Guo S Y, Xie M S, et al. Fractal characteristics of daily discharge in different scales watersheds [J]. Ying yong sheng tai xue bao= The journal of applied ecology/Zhongguo sheng tai xue xue hui, Zhongguo ke xue yuan Shenyang ying yong sheng tai yan jiu suo zhu ban,2011,22(1):159.
[91]Bof L H N, Pruski F F, da Silva L M C, et al. Analysis of Appropriate Timescales for Water Diversion Permits in Brazil [J]. Environmental management,2013,51(2): 492-500.
[92]徐国宾,杨志达.基于最小熵产生与耗散结构和混沌理论的河床演变分析[J].水利学报,2012,43(8)：948-956.
[93]Ghilardi P, Rosso R. Comment on "Chaos in rainfall" by I. Rodriguez-Iturbe et al[J]. Water Resources Research,1990,26(8):1837-1839.
[94]Koutsoyiannis D, Pachakis D. Deterministic chaos versus stochasticity in analysis and modeling of point rainfall series [J]. Journal of Geophysical Research:Atmospheres (1984-2012),1996,101(D21):26441-26451.
[95]Pasternack G B. Does the river run wild? Assessing chaos in hydrological systems [J]. Advances in Water Resources,1999,23(3):253-260.
[96]Schertzer D, TCHIGUIRINSKAIA I, LOVEJOY S, et al. Which chaos in the rainfall-runoff process? [J]. Hydrological Sciences-Journal-des Sciences Hydrologiques,2002,47(1).
[97]徐静,任立良,阮晓红.不同地形复杂度下的水文尺度效应研究[J].水土保持研究,2009,17(1)：35-39
[98]Tsonis A A. Probing the linearity and nonlinearity in the transitions of the atmospheric circulation [J]. Nonlinear Processes in Geophysics,2001,8(6):341-345.
[99]孝芳.水文学的机遇及砬着重研究的若干领域[J].中国水利,2004,7：22-24.
[100]李双成,蔡运龙.地理尺度转换若干问题的初步探讨[J].地理研究,2005,24：11-18.
[101]张东辉,张金存,刘万贵.关于水文学中非线性效应的探讨[J].水科学进展,2007,18(5)：776-784.
[102]桑燕芳,王中根,刘昌明.水文时间序列分析方法研究[J].地理科学进展,32(1)：20-30
[103]赵辉,郭索彦,解明曙,雷廷武.不同尺度流域日径流分形特征[J].应用生态学报,2011,22(1)：159-164.
[104]李红霞,许士国,范垂仁.月径流序列的混沌特征识别及Volterra自适应预测法的应用[J].水利学报,38(6)：760-767.
[105]陈仁升,康尔泗,杨建平,张济世.黑河出山径流的非线性特征分析[J].冰川冻 土,24(3)：292-298.
[106]陈莹,许有鹏,尹义星,刘星才.长江干流日径流序列的多重分形特征.地理研究,2008,27(4)：819-828.
[107]Wang C T, Gupta V K. A geomorphologic synthesis of nonlinearity in surface runoff [J]. Water Resources Research,1981,17(3):545-554.
[108]丁晶,邓育仁,吴伯贤,杨荣富.洪水浑沌分析[J].成都科技大学学报,1993,73(6)：1-5.
[109]Robinson J S, Sivapalan M. An investigation into the physical causes of scaling and heterogeneity of regional flood frequency [J]. Water Resources Research,1997,33(5): 1045-1059.
[110]王海燕,盛昭瀚,混沌时间序列相空间重构参数的选取方法[J].东南大学学报(自然科学版),2000,30(5),113-117.
[111]陈铿,韩伯棠.混沌时间序列分析中的相空间重构技术综述[J].计算机科学,2005,32(4)：67-70.
[112]丁胜祥,杨新意.宜昌站月径流时间序列的混沌特性分析[J].人民长江,2009,40(2),32-35.
[113]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究[J].计算机工程与应用,2006,26：162-164.
[114]Gottwald G A, Melbourne I. On the implementation of the 0-1 test for chaos [J]. SIAM Journal on Applied Dynamical Systems,2009,8(1):129-145.
[115]Gottwald G A, Melbourne I. On the validity of the 0-1 test for chaos [J]. arXiv preprint arXiv:0906.1415,2009.
[116]王红瑞,宋宇,刘昌明,等.混沌理论及在水科学中的应用与存在的问题[J].水科学进展,2004,15(3).
[117]卢山.基于非线性动力学的金融时间序列预测技术研究[D].东南大学,2006.
[118]陈敏,叶晓舟.混沌时间序列的判定方法比较[J].信息技术,2008,6：23-26.
[119]刘东林,帅典勋.网络流量模型的非线性特征量的提取及分析[J].电子学报,31(12)：1866-1869.
[120]张建业,潘泉,梁建海.FDR飞行数据的相空间重构及混沌特征分析[J].空军工程大学学报(自然科学版),2009,10(4)：6-10.
[121]Casdagli M C. Recurrence plots revisited [J]. Physica D:Nonlinear Phenomena,1997, 108(1):12-44.
[122]Marwan N, Wessel N, Meyerfeldt U, et al. Recurrence-plot-based measures of complexity and their application to heart-rate-variability data [J]. Physical Review E, 2002,66(2):026702.
[123]Trulla L L, Giuliani A, Zbilut J P, et al. Recurrence quantification analysis of the logistic equation with transients [J]. Physics Letters A,1996,223(4):255-260.
[124]Riley M A, Balasubramaniam R, Turvey M T. Recurrence quantification analysis of postural fluctuations [J]. Gait & Posture,1999,9(1):65-78.
[125]Zbilut J P, Thomasson N, Webber C L. Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals [J]. Medical engineering & physics,2002,24(1):53-60.
[126]凌继平,黄定东,邓异,等.基于递归图和近似熵的水下目标特征提取方法[J].计算机与数字工程,2011,39(11)：147-150.
[127]Webber Jr C L, Zbilut J P. Recurrence quantification analysis of nonlinear dynamical systems [J]. Tutorials in contemporary nonlinear methods for the behavioral sciences, 2005:26-94.
[128]Zbilut J P, Giuliani A, Webber Jr C L. Recurrence quantification analysis as an empirical test to distinguish relatively short deterministic versus random number series [J]. Physics Letters A,2000,267(2):174-178.
[129]Yang J Y, Peng Z L, Yu Z G, et al. Prediction of protein structural classes by recurrence quantification analysis based on chaos game representation [J]. Journal of theoretical biology,2009,257(4):618-626.
[130]Li X, Ouyang G, Yao X, et al. Dynamical characteristics of pre-epileptic seizures in rats with recurrence quantification analysis [J]. Physics Letters A,2004,333(1): 164-171.
[131]Zbilut J P, Webber C L. Recurrence quantification analysis [J]. Wiley Encyclopedia of Biomedical Engineering,2006.
[132]FABRETTI A, Ausloos M. Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market inidices [J]. International Journal of Modern Physics C,2005,16(05):671-706.
[133]ACHARYA U R, Sree S V, CHATTOPADHYAY S, et al. Application of recurrence quantification analysis for the automated identification of epileptic EEG signals [J]. International journal of neural systems,2011,21(03):199-211.
[134]Marwan N, Carmen Romano M, Thiel M, et al. Recurrence plots for the analysis of complex systems [J]. Physics Reports,2007,438(5):237-329.
[135]杨栋,任新伟.基于递归分析的振动信号非平稳性评价[J].振动与冲击,2011,30(12),39-43.
[136]闫源江,胡光波,周勇.舰船辐射噪声的非线性和确定性检验[J].舰船电子工程,2010,03(10)：150-153.
[137]陈静,李亚安,王东海.基于递归分析的水声信号处理[J].哈尔滨工程大学学报,2006,27(5)：649-652.
[138]王冬梅,黄春辉,谭平,王延军,李雷.递归特性分析在油气水三相流中的应用[J].石油仪器,25(6)：50-54.
[139]闫润强.语音信号动力学特性递归分析[D].上海：上海交通大学,2006.
[140]董典帅.聚合物绝缘材料耐电痕性研究及其非线性分析[D].2008
[141]洪文鹏,周云龙,刘燕.管束间压差波动信号的递归特性分析[J].中国机电工程学报,2011,31(23)：74-78
[142]金宁德,陈万鹏.混沌递归分析在油水两相流流型识别中的应用[J].化工学报,2006,57(2)：274-280.
[143]金宁德,郑桂波,陈万鹏.研究论文气液两相流电导波动信号的混沌递归特性分析[J].化工学报,2007,58(5).
[144]李新杰,胡铁松,董秀明.递归图法在径流时间序列分析中的应用[J].武汉大学学报(工学版),2013.46(1)：62-66.
[145]洪文鹏,周云龙,刘燕.管束间压差波动信号的递归特性分析[J].中国机电工程学报,2011.31(23)：74-78
[146]Parrott L. Analysis of simulated long-term ecosystem dynamics using visual recurrence analysis [J]. Ecological Complexity,2004,1(2):111-125.
[147]Kononov E. Visual recurrence analysis [J]. VRA version,2004,4.
[148]董芳.气液两相流流动结构多尺度及非线性特性分析[D].天津大学,2007.
[149]白宝丹.基于递归复杂网络的房颤预测分析方法研究[D].复旦大学,2012.
[150]欧阳高翔.癫痫脑电信号的非线性特征识别与分析[D].燕山大学,2010.
[151]Bandt C, Pompe B. Permutation entropy:A natural complexity measure for time series[J]. Physical Review Letters,2002,88(17):174102.
[152]Marwan N, Carmen Romano M, Thiel M, et al. Recurrence plots for the analysis of complex systems [J]. Physics Reports,2007,438(5):237-329.
[153]Jordan D, Stockmanns G, Kochs E F, et al. Electroencephalographic order pattern analysis for the separation of consciousness and unconsciousness:an analysis of approximate entropy, permutation entropy, recurrence rate, and phase coupling of order recurrence plots [J]. Anesthesiology,2008,109(6):1014-1022.
[154]Groth A. Visualization of coupling in time series by order recurrence plots [J]. Physical Review E,2005,72(4):046220.
[155]唐德华.短时交通流特性及状态转变研究[D].华南理工大学,2011
[156]宋晓,李平,徐公林,李树卿,郭家虎.电能质量扰动的递归定量分析[J].电测与仪表,2012,49(561)：4-9.
[157]肖涵,李友荣,吕勇.基于递归定量分析与高斯混合模型的齿轮故障识别[J].振动工程学报,24(1)：84-88.
[158]孙斌,李超,周云龙.基于递归定量特征的气-液两相流流型融合识别[J].核动力工程,2009,30(6)：57-62.
[159]尹少华,杨基海,梁政,等.基于递归量化分析的表面肌电特征提取和分类[J].中国科学技术大学学报,2006,5：550-555.
[160]洪文鹏,刘燕,周云龙.气液两相流流型图像信息熵递归特性分析[J].热能动力工程,2011,26(5)：538-542.
[161]周云龙,陈飞.水平气液两相流流型空间图像信息复杂性测度分析[J]化工学报,2008,59(1)：64-68.
[162]高忠科,金宁德等.多元时间序列复杂网络流型动力学分析[J].物理学报,2012,61(12),120510-120519.
[163]高忠科.两相流流型复杂网络非线性动力学特征研究[D].天津大学,2010.
[164]Sen A K, Longwic R, Litak G, et al. Analysis of cycle-to-cycle pressure oscillations in a diesel engine[J]. Mechanical Systems and Signal Processing,2008,22(2): 362-373.
[165]Hosmer D W, Lemeshow S. Applied logistic regression [M]. Wiley-Interscience, 2004.
[166]吕勇,徐金梧,李友荣.递归图和近似熵在设备故障信号复杂度分析中的应用[J].2006,机械强度,28(3)：317-321.
[167]Von Bloh W, Romano M C, Thiel M. Long-term predictability of mean daily temperature data[J]. Nonlinear Processes in Geophysics,2005,12(4):471-479.
[168]赵鹏,周云龙,孙斌.递归定量分析在离心泵故障诊断中的运用[J].振动、测试与诊断,2010,30(6)：612-617.
[169]汪小帆,李翔,陈关荣.复杂网络理论及其应用[M].清华大学出版社有限公司,2006.
[170]陆履亨.网络信息资源管理概论[M].上海人民出版社,2003.
[171]周涛,柏文洁,汪秉宏,等.复杂网络研究概述[J].物理,2005,34(01)：0.
[172]吴彤.复杂网络研究及其意义[J].哲学研究,2004(8)：58-63.
[173]郭雷,许晓鸣.复杂网络[M].上海科技教育出版社,2006.
[174]刘涛,陈忠,陈晓荣.复杂网络理论及其应用研究概述[J].系统工程,2005,6：000.
[175]孙惠泉.图论及其应用[M].科学出版社,2004.
[176]Erdos P, Renyi A. On the strength of connectedness of a random graph [J]. Acta Mathematica Hungarica,1961,12(1):261-267.
[177]杜海峰,李树茁,悦中山,等.小世界网络与无标度网络的社区结构研究[J].物理学报,2007,56(12)：6886-6893.
[178]Watts D J, Strogatz S H. Collective dynamics of'small-world'networks [J]. nature, 1998,393(6684):440-442.
[179]Barabasi A L, Albert R. Emergence of scaling in random networks [J]. science,1999, 286(5439):509-512.
[180]高自友,赵小梅,黄海军,等.复杂网络理论与城市交通系统复杂性问题的相关研究[J].交通运输系统工程与信息,2006,6(3)：41-47.
[181]方锦清.网络科学的理论模型探索及其进展[J].科技导报,2006,24(12)：67-72.
[182]吴金闪,狄增如.从统计物理学看复杂网络研究[J].物理学进展,2004,24(1)：18-46.
[183]Gang Y, Tao Z, Jie W, et al. Epidemic spread in weighted scale-free networks [J]. Chinese Physics Letters,2005,22(2):510.
[184]俞辉,王永骥,程磊.基于有向网络的智能群体群集运动控制[J].控制理论与应用,2007,24(1)：79-83.
[185]谭跃进,吴俊,邓宏钟.复杂网络中节点重要度评估的节点收缩方法[J].系统工程理论与实践,2006,26(11)：79-83.
[186]赫南,李德毅,淦文燕,等.复杂网络中重要性节点发掘综述[J].计算机科学,2007,34(12)：1-5.
[187]刘宏鲲,周涛.中国城市航空网络的实证研究与分析[J].物理学报,2007,56(1)：106-112.
[188]李季,汪秉宏,蒋品群,等.节点数加速增长的复杂网络生长模型[J].物理学报,2006,55(8)：4051-4057.
[189]杨博,刘大有,Jiming L, et al.复杂网络聚类方法[J].软件学报,2009,20(1)：54-66.
[190]Watts D J, Strogatz S H. Collective dynamics of'small-world'networks [J]. Nature, 1998,393(6684):440-442.
[191]张宇,张宏莉,方滨兴.Internet拓扑建模综述[J].软件学报,2004,15(8)：1220-1226.
[192]张培培,何阅,周涛,等.一个描述合作网络顶点度分布的模型[J].物理学报,2006,55(1)：60-67.
[193]杜海峰,李树茁,悦中山,等.小世界网络与无标度网络的社区结构研究[J].物理学报,2007,56(12)：6886-6893.
[194]Barabasi A L, Albert R. Emergence of scaling in random networks [J]. science,1999, 286(5439):509-512.
[195]车宏安,顾基发.无标度网络及其系统科学意义[J].系统工程理论与实践,2004,24(4)：11-16.
[196]Girvan M, Newman M E J. Community structure in social and biological networks [J]. Proceedings of the National Academy of Sciences,2002,99(12):7821-7826.
[197]Newman M E J, Girvan M. Finding and evaluating community structure in networks [J]. Physical review E,2004,69(2):026113.
[198]方锦清.非线性网络的动力学复杂性研究的若干进展[J].自然科学进展,2007,17(7)：841-857.
[199]李晓佳,张鹏,狄增如,等.复杂网络中的社团结构[J].复杂系统与复杂性科学,2008,5(3)：19-42.
[200]Hartigan J A, Wong M A. Algorithm AS 136:A k-means clustering algorithm[J]. Journal of the Royal Statistical Society. Series C (Applied Statistics),1979,28(1): 100-108.
[201]刘婷,胡宝清.基于聚类分析的复杂网络中的社团探测[J].复杂系统与复杂性科学,2007,4(1)：28-35.
[202]Zhong-Ke G, Ning-De J.两相流流型复杂网络社团结构及其统计特性[J].物理学报,2008,57(11)：6909-6920.
[203]Clauset A, Newman M E J, Moore C. Finding community structure in very large networks[J]. Physical review E,2004,70(6):066111.
[204]王立敏,高学东,宫雨,等.基于相对密度的社团结构探测算法[J].计算机工程,2009,35(1)：117-119.
[205]骆志刚,丁凡,蒋晓舟,等.复杂网络社团发现算法研究新进展[J].国防科技大学学报,2011,33(1)：47-52.
[206]Gao Z, Jin N. Complex network from time series based on phase space reconstruction [J]. Chaos:An interdisciplinary journal of nonlinear science,2009,19(3): 033137-033149.
[2]王兴元.复杂非线性系统中的混沌[M].电子工业出版社,2003.
[3]陈关荣,吕金虎.Lorenz系统族的动力学分析,控制与同步[M].科学出版社,2003.
[4]张济世,刘立昱,程中山.统计水文学[M].黄河水利出版社,2006.
[5]李彦彬.河川径流的混沌特征和预测研究[D].西安理工大学,2009.
[6]洛伦兹EN.混沌的本质[J].北京：气象出版版社,1997：152-159.
[7]刘建香.复杂网络及其在国内研究进展的综述[J].系统科学学报,2009(4).
[8]陶瑾,陈晓红,汪丽娜,谢毅文.北江流域径流时间序列的分形特征解析[J].中山大学学报,2011,50(5)：148-152.
[9]魏茹.多元混沌时间序列的变量选择及预测方法研究[D].大连理工大学,2007.
[10]佟春生.复杂性理论在河川径流时间序列分析中的应用研究[D].西安理工大学,2005.
[11]米红,张文璋.实用现代统计分析方法与SPSS应用[J].北京：当代中国出版社,2000,10.
[12]刘洪,李必强.基于混沌吸引子的时间序列预测[J].系统工程与电子技术,1997,19(2)：23-28.
[13]韩敏.混沌时间序列预测理论与方法[M].中国水利水电出版社,2007.
[14]黄国如,芮孝芳.流域降雨径流时间序列的混沌识别及其预测研究进展[J].水科学进展,2004,15(2)：255-260.
[15]Rodriguez-Iturbe I, Febres De Power B, Sharifi M B, et al. Chaos in rainfall [J]. Water Resources Research,1989,25(7):1667-1675.
[16]夏荣尧.基于ARIMA模型的我国通货膨胀预测研究[D].湖南大学,2009.
[17]Wilcox B P, Seyfried M S, Matison T H. Searching for chaotic dynamics in snowmelt runoff [J]. Water Resources Research,1991,27(6):1005-1010.
[18]Jayawardena A W, Lai F. Analysis and prediction of chaos in rainfall and stream flow time series [J]. Journal of Hydrology,1994,153(1):23-52.
[19]Sivakumar B, Liong S Y, Liaw C Y. EVIDENCE OF CHAOTIC BEHAVIOR IN SINGAPORE RAINFALL1 [J]. JAWRA Journal of the American Water Resources Association,1998,34(2):301-310.
[20]Sivakumar B, Phoon K K, Liong S Y, et al. A systematic approach to noise reduction in chaotic hydrological time series [J]. Journal of hydrology,1999,219(3):103-135.
[21]Sivakumar B, Berndtsson R, Olsson J, et al. Evidence of chaos in the rainfall-runoff process [J]. Hydrological Sciences Journal,2001,46(1):131-145.
[22]Sivakumar B, Sorooshian S, Gupta H V, et al. A chaotic approach to rainfall disaggregation [J]. Water Resources Research,2001,37(1):61-72.
[23]Sivakumar B. Chaos in rainfall:variability, temporal scale and zeros [J]. Journal of Hydroinformatics,2005,7:175-184.
[24]Wang W, Vrijling J K, Van Gelder P H, et al. Testing for nonlinearity of streamflow processes at different timescales [J]. Journal of Hydrology,2006,322(1):247-268.
[25]Ng W W, Panu U S, Lennox W C. Chaos based analytical techniques for daily extreme hydrological observations [J]. Journal of Hydrology,2007,342(1):17-41.
[26]Zhang L, Xia J, Song X, et al. Similarity model of chaos phase space and its application in mid-and long-term hydrologic prediction [J]. Kybernetes,2009,38(10): 1835-1842.
[27]Ghorbani M A, Kisi O, Aalinezhad M. A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods [J]. Applied Mathematical Modelling,2010,34(12):4050-4057.
[28]Dhanya C T, Nagesh Kumar D. Nonlinear ensemble prediction of chaotic daily rainfall [J]. Advances in Water Resources,2010,33(3):327-347.
[29]Dhanya C T, Nagesh Kumar D. Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs [J]. Journal of Hydrology,2011,403(3):292-306.
[30]Khatibi R, Sivakumar B, Ghorbani M A, et al. Investigating chaos in river stage and discharge time series [J]. Journal of Hydrology,2012,414:108-117.
[31]丁晶,邓育仁,吴伯贤.洪水混沌分析[J].水资源研究,1992,13(3)：14-18.
[32]王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析[J].水科学进展,1994,5(2)：87-94.
[33]傅军,丁晶,邓育仁.洪水混沌特性初步研究[J].水科学进展,1996,7(3)：226-230.
[34]赵永龙,丁晶,邓育仁.相空间小波网络模型及其在水文中长期预测中的应用[J].水科学进展,1999,9(3)：252-257.
[35]温权,张士军,张周胜.探求径流序列中的混沌特征[J].水电能源科学,1999,17(1)：21-23.
[36]赵永龙,常晓青,丁晶,邓育仁.水文动力系统重建相空间嵌入维数研究[J].人民长江,1999,30：43-45.
[37]陈云浩,史培军,李晓兵.不同热力背景对城市降雨(暴雨)的影响(Ⅱ)-降雨时序的混沌分析[J].2001,10(3)：20-25.
[38]袁鹏,李谓新,王文圣,丁晶.月降雨量时间序列中的混沌现象[J].四川大学学报(工程科学报),2002,34(1)16-19.
[39]李眉眉,丁晶,王文圣.基于混沌理论的径流降尺度分析[J].四川大学学报(工程科学版),2004,3：003.
[40]李荣峰,沈冰,张金凯.基于相空间重构的水文自记忆预测模型[J].水利学报,2006,5：583-591.
[41]于国荣,夏自强.混沌时间序列支持向量机模型及其在径流预测中应用[J].水科学进展,2008,19(1)：116-122.
[42]Porporato A, Ridolfi L. Clues to the existence of deterministic chaos in river flow [J]. International Journal of modern physics B,1996,10(15):1821-1862.
[43]Sivakumar B. Correlation dimension estimation of hydrological series and data size requirement:myth and reality/Estimation de la dimension de correlation de series hydrologiques et taille necessaire du jeu de donnees:mythe et realite [J]. Hydrological sciences journal,2005,50(4).
[44]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择[J].系统仿真学报,2007,19(11)：2527-2530.
[45]徐自励,王一扬,周激流.估计非线性时间序列嵌入延迟时间和延迟时间窗的C-C平均方法[J].四川大学学报(工程科学版),2007,39(1)：151-155.
[46]Osborne A R, Provenzale A. Finite correlation dimension for stochastic systems with power-law spectra [J]. Physica D:Nonlinear Phenomena,1989,35(3):357-381.
[47]Rapp P E, Albano A M, Schmah T I, et al. Filtered noise can mimic low-dimensional chaotic attractors [J]. Physical review E,1993,47(4):2289.
[48]Provenzale A, Osborne A R, Soj R. Convergence of the K2 entropy for random noises with power law spectra [J]. Physica D:Nonlinear Phenomena,1991,47(3):361-372.
[49]Gottwald G A, Melbourne I. On the implementation of the 0-1 test for chaos [J]. SIAM Journal on Applied Dynamical Systems,2009,8(1):129-145.
[50]Skokos C, Antonopoulos C, Bountis T C, et al. Detecting order and chaos in Hamiltonian systems by the SALI method [J]. Journal of Physics A:Mathematical and General,2004,37(24):6269.
[51]Martinsen-Burrell N, Julien K, Petersen M R, et al. Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices [J]. Physics of Fluids,2006,18:057101.
[52]Gottwald G A, Melbourne I. Testing for chaos in deterministic systems with noise [J]. Physica D:Nonlinear Phenomena,2005,212(1):100-110.
[53]Falconer I, Gottwald G A, Melbourne I, et al. Application of the 0-1 test for chaos to experimental data [J]. SIAM Journal on Applied Dynamical Systems,2007,6(2): 395-402.
[54]Eckmann J P, Kamphorst S O, Ruelle D. Recurrence plots of dynamical systems [J]. EPL (Europhysics Letters),1987,4(9):973.
[55]Trulla L L, Giuliani A, Zbilut J P, et al. Recurrence quantification analysis of the logistic equation with transients [J]. Physics Letters A,1996,223(4):255-260.
[56]Yang Y, Yang H. Complex network-based time series analysis [J]. Physica A: Statistical Mechanics and its Applications,2008,387(5):1381-1386.
[57]汪小帆,刘亚冰.复杂网络中的社团结构算法综述[J].电子科技大学学报,2009,38(5)：537-543.
[58]郝柏林.复杂性的刻画与复杂性科学[J].科学,1999,51(3)：3-8.
[59]李国良.混沌理论及其在水文时间序列中的应用[D].东北农业大学,2007.
[60]Li T Y, Yorke J A. Period three implies chaos [J]. The American Mathematical Monthly,1975,82(10):985-992.
[61]Devaney R L. An introduction to chaotic dynamical systems [J].2003.
[62]李健.动力系统的复杂性及其应用[D].中国科学技术大学,2012.
[63]唐强.基于复杂网络理论的径流时间序列非线性性质研究[D].武汉大学,2011.
[64]张丽娟.离散动力系统的混沌判定和扰动[D].山东大学,2011
[65]郑金.短期电力负荷预测方法研究[D].2012.
[66]Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length [J]. Physica D:Nonlinear Phenomena, 1996,95(1):13-28.
[67]王抵修.地学数据分析中的相空间重构预测方法研究[D].吉林大学,2008.
[68]Takens F. Detecting strange attractors in turbulence [M]. Dynamical systems and turbulence, Warwick 1980. Springer Berlin Heidelberg,1981:366-381.
[69]甘建超.混沌信号处理在雷达和通信对抗中的应用[D].电子科技大学,2004
[70]刘力.三峡流域径流特性分析及预测研究[D].华中科技大学,2009.
[71]Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times, and embedding windows [J]. Physica D:Nonlinear Phenomena,1999,127(1):48-60.
[72]刘文博.混沌时间序列分析与计算方法及应用研究[D].大连理工大学,2008
[73]杨世锡.柯尔莫哥洛夫嫡及其在故障诊断中的应用[J].机械科学与技术,2000, 19(1)：6-8.
[74]Kennel M B, Brown R, Abarbanel H D I. Determining embedding dimension for phase-space reconstruction using a geometrical construction [J]. Physical review A, 1992,45(6):3403.
[75]许小可.基于非线性分析的海杂波处理与目标检测[D].大连海事大学,2008.
[76]Cao L. Practical method for determining the minimum embedding dimension of a scalar time series [J]. Physica D:Nonlinear Phenomena,1997,110(1):43-50.
[77]Grassberger P, Procaccia I. Characterization of strange attractors[J]. Physical review letters,1983,50(5):346-349.
[78]于青.关联维数计算的分析研究[J].天津理工学院学报,2004,20(4)：60-62.
[79]Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series[J]. Physica D:Nonlinear Phenomena,1985,16(3):285-317.
[80]Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets [J]. Physica D:Nonlinear Phenomena,1993, 65(1):117-134.
[81]余波,李应红,张朴.关联维数和Kofmognrov嫡在航空发动机故障诊断中的应用[J].航空动力学报,2006.2
[82]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究[J].计算机工程与应用,2006,21：162-164.
[83]王蕾.基于互信息网络模型的冰雹回波时间序列知识发现[D].天津大学,2008.
[84]李新杰,胡铁松,郭旭宁,等.0—1测试方法的径流时间序列混沌特性应用[J].水科学进展,2012,23(6)：861-868.
[85]王云琦,齐实,孙阁,等.气候与土地利用变化对流域水资源的影响：以美国北卡罗莱纳州Trent流域为例[J].水科学进展,2011,22(1)：51-58.
[86]涂新军,陈晓宏,张强,等.东江径流年内分配特征及影响因素贡献分解[J].水科学进展,2012,23(4)：465-474.
[87]Ghorbani M A, Kisi O, Aalinezhad M. A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods [J]. Applied Mathematical Modelling,2010,34(12):4050-4057.
[88]Ke-Hui S, Xuan L, Cong-Xu Z. The 0-1 test algorithm for chaos and its applications [J]. Chinese Physics B,2010,19(11):110510.
[89]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2)：55-58.
[90]Zhao H, Guo S Y, Xie M S, et al. Fractal characteristics of daily discharge in different scales watersheds [J]. Ying yong sheng tai xue bao= The journal of applied ecology/Zhongguo sheng tai xue xue hui, Zhongguo ke xue yuan Shenyang ying yong sheng tai yan jiu suo zhu ban,2011,22(1):159.
[91]Bof L H N, Pruski F F, da Silva L M C, et al. Analysis of Appropriate Timescales for Water Diversion Permits in Brazil [J]. Environmental management,2013,51(2): 492-500.
[92]徐国宾,杨志达.基于最小熵产生与耗散结构和混沌理论的河床演变分析[J].水利学报,2012,43(8)：948-956.
[93]Ghilardi P, Rosso R. Comment on "Chaos in rainfall" by I. Rodriguez-Iturbe et al[J]. Water Resources Research,1990,26(8):1837-1839.
[94]Koutsoyiannis D, Pachakis D. Deterministic chaos versus stochasticity in analysis and modeling of point rainfall series [J]. Journal of Geophysical Research:Atmospheres (1984-2012),1996,101(D21):26441-26451.
[95]Pasternack G B. Does the river run wild? Assessing chaos in hydrological systems [J]. Advances in Water Resources,1999,23(3):253-260.
[96]Schertzer D, TCHIGUIRINSKAIA I, LOVEJOY S, et al. Which chaos in the rainfall-runoff process? [J]. Hydrological Sciences-Journal-des Sciences Hydrologiques,2002,47(1).
[97]徐静,任立良,阮晓红.不同地形复杂度下的水文尺度效应研究[J].水土保持研究,2009,17(1)：35-39
[98]Tsonis A A. Probing the linearity and nonlinearity in the transitions of the atmospheric circulation [J]. Nonlinear Processes in Geophysics,2001,8(6):341-345.
[99]孝芳.水文学的机遇及砬着重研究的若干领域[J].中国水利,2004,7：22-24.
[100]李双成,蔡运龙.地理尺度转换若干问题的初步探讨[J].地理研究,2005,24：11-18.
[101]张东辉,张金存,刘万贵.关于水文学中非线性效应的探讨[J].水科学进展,2007,18(5)：776-784.
[102]桑燕芳,王中根,刘昌明.水文时间序列分析方法研究[J].地理科学进展,32(1)：20-30
[103]赵辉,郭索彦,解明曙,雷廷武.不同尺度流域日径流分形特征[J].应用生态学报,2011,22(1)：159-164.
[104]李红霞,许士国,范垂仁.月径流序列的混沌特征识别及Volterra自适应预测法的应用[J].水利学报,38(6)：760-767.
[105]陈仁升,康尔泗,杨建平,张济世.黑河出山径流的非线性特征分析[J].冰川冻 土,24(3)：292-298.
[106]陈莹,许有鹏,尹义星,刘星才.长江干流日径流序列的多重分形特征.地理研究,2008,27(4)：819-828.
[107]Wang C T, Gupta V K. A geomorphologic synthesis of nonlinearity in surface runoff [J]. Water Resources Research,1981,17(3):545-554.
[108]丁晶,邓育仁,吴伯贤,杨荣富.洪水浑沌分析[J].成都科技大学学报,1993,73(6)：1-5.
[109]Robinson J S, Sivapalan M. An investigation into the physical causes of scaling and heterogeneity of regional flood frequency [J]. Water Resources Research,1997,33(5): 1045-1059.
[110]王海燕,盛昭瀚,混沌时间序列相空间重构参数的选取方法[J].东南大学学报(自然科学版),2000,30(5),113-117.
[111]陈铿,韩伯棠.混沌时间序列分析中的相空间重构技术综述[J].计算机科学,2005,32(4)：67-70.
[112]丁胜祥,杨新意.宜昌站月径流时间序列的混沌特性分析[J].人民长江,2009,40(2),32-35.
[113]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究[J].计算机工程与应用,2006,26：162-164.
[114]Gottwald G A, Melbourne I. On the implementation of the 0-1 test for chaos [J]. SIAM Journal on Applied Dynamical Systems,2009,8(1):129-145.
[115]Gottwald G A, Melbourne I. On the validity of the 0-1 test for chaos [J]. arXiv preprint arXiv:0906.1415,2009.
[116]王红瑞,宋宇,刘昌明,等.混沌理论及在水科学中的应用与存在的问题[J].水科学进展,2004,15(3).
[117]卢山.基于非线性动力学的金融时间序列预测技术研究[D].东南大学,2006.
[118]陈敏,叶晓舟.混沌时间序列的判定方法比较[J].信息技术,2008,6：23-26.
[119]刘东林,帅典勋.网络流量模型的非线性特征量的提取及分析[J].电子学报,31(12)：1866-1869.
[120]张建业,潘泉,梁建海.FDR飞行数据的相空间重构及混沌特征分析[J].空军工程大学学报(自然科学版),2009,10(4)：6-10.
[121]Casdagli M C. Recurrence plots revisited [J]. Physica D:Nonlinear Phenomena,1997, 108(1):12-44.
[122]Marwan N, Wessel N, Meyerfeldt U, et al. Recurrence-plot-based measures of complexity and their application to heart-rate-variability data [J]. Physical Review E, 2002,66(2):026702.
[123]Trulla L L, Giuliani A, Zbilut J P, et al. Recurrence quantification analysis of the logistic equation with transients [J]. Physics Letters A,1996,223(4):255-260.
[124]Riley M A, Balasubramaniam R, Turvey M T. Recurrence quantification analysis of postural fluctuations [J]. Gait & Posture,1999,9(1):65-78.
[125]Zbilut J P, Thomasson N, Webber C L. Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals [J]. Medical engineering & physics,2002,24(1):53-60.
[126]凌继平,黄定东,邓异,等.基于递归图和近似熵的水下目标特征提取方法[J].计算机与数字工程,2011,39(11)：147-150.
[127]Webber Jr C L, Zbilut J P. Recurrence quantification analysis of nonlinear dynamical systems [J]. Tutorials in contemporary nonlinear methods for the behavioral sciences, 2005:26-94.
[128]Zbilut J P, Giuliani A, Webber Jr C L. Recurrence quantification analysis as an empirical test to distinguish relatively short deterministic versus random number series [J]. Physics Letters A,2000,267(2):174-178.
[129]Yang J Y, Peng Z L, Yu Z G, et al. Prediction of protein structural classes by recurrence quantification analysis based on chaos game representation [J]. Journal of theoretical biology,2009,257(4):618-626.
[130]Li X, Ouyang G, Yao X, et al. Dynamical characteristics of pre-epileptic seizures in rats with recurrence quantification analysis [J]. Physics Letters A,2004,333(1): 164-171.
[131]Zbilut J P, Webber C L. Recurrence quantification analysis [J]. Wiley Encyclopedia of Biomedical Engineering,2006.
[132]FABRETTI A, Ausloos M. Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market inidices [J]. International Journal of Modern Physics C,2005,16(05):671-706.
[133]ACHARYA U R, Sree S V, CHATTOPADHYAY S, et al. Application of recurrence quantification analysis for the automated identification of epileptic EEG signals [J]. International journal of neural systems,2011,21(03):199-211.
[134]Marwan N, Carmen Romano M, Thiel M, et al. Recurrence plots for the analysis of complex systems [J]. Physics Reports,2007,438(5):237-329.
[135]杨栋,任新伟.基于递归分析的振动信号非平稳性评价[J].振动与冲击,2011,30(12),39-43.
[136]闫源江,胡光波,周勇.舰船辐射噪声的非线性和确定性检验[J].舰船电子工程,2010,03(10)：150-153.
[137]陈静,李亚安,王东海.基于递归分析的水声信号处理[J].哈尔滨工程大学学报,2006,27(5)：649-652.
[138]王冬梅,黄春辉,谭平,王延军,李雷.递归特性分析在油气水三相流中的应用[J].石油仪器,25(6)：50-54.
[139]闫润强.语音信号动力学特性递归分析[D].上海：上海交通大学,2006.
[140]董典帅.聚合物绝缘材料耐电痕性研究及其非线性分析[D].2008
[141]洪文鹏,周云龙,刘燕.管束间压差波动信号的递归特性分析[J].中国机电工程学报,2011,31(23)：74-78
[142]金宁德,陈万鹏.混沌递归分析在油水两相流流型识别中的应用[J].化工学报,2006,57(2)：274-280.
[143]金宁德,郑桂波,陈万鹏.研究论文气液两相流电导波动信号的混沌递归特性分析[J].化工学报,2007,58(5).
[144]李新杰,胡铁松,董秀明.递归图法在径流时间序列分析中的应用[J].武汉大学学报(工学版),2013.46(1)：62-66.
[145]洪文鹏,周云龙,刘燕.管束间压差波动信号的递归特性分析[J].中国机电工程学报,2011.31(23)：74-78
[146]Parrott L. Analysis of simulated long-term ecosystem dynamics using visual recurrence analysis [J]. Ecological Complexity,2004,1(2):111-125.
[147]Kononov E. Visual recurrence analysis [J]. VRA version,2004,4.
[148]董芳.气液两相流流动结构多尺度及非线性特性分析[D].天津大学,2007.
[149]白宝丹.基于递归复杂网络的房颤预测分析方法研究[D].复旦大学,2012.
[150]欧阳高翔.癫痫脑电信号的非线性特征识别与分析[D].燕山大学,2010.
[151]Bandt C, Pompe B. Permutation entropy:A natural complexity measure for time series[J]. Physical Review Letters,2002,88(17):174102.
[152]Marwan N, Carmen Romano M, Thiel M, et al. Recurrence plots for the analysis of complex systems [J]. Physics Reports,2007,438(5):237-329.
[153]Jordan D, Stockmanns G, Kochs E F, et al. Electroencephalographic order pattern analysis for the separation of consciousness and unconsciousness:an analysis of approximate entropy, permutation entropy, recurrence rate, and phase coupling of order recurrence plots [J]. Anesthesiology,2008,109(6):1014-1022.
[154]Groth A. Visualization of coupling in time series by order recurrence plots [J]. Physical Review E,2005,72(4):046220.
[155]唐德华.短时交通流特性及状态转变研究[D].华南理工大学,2011
[156]宋晓,李平,徐公林,李树卿,郭家虎.电能质量扰动的递归定量分析[J].电测与仪表,2012,49(561)：4-9.
[157]肖涵,李友荣,吕勇.基于递归定量分析与高斯混合模型的齿轮故障识别[J].振动工程学报,24(1)：84-88.
[158]孙斌,李超,周云龙.基于递归定量特征的气-液两相流流型融合识别[J].核动力工程,2009,30(6)：57-62.
[159]尹少华,杨基海,梁政,等.基于递归量化分析的表面肌电特征提取和分类[J].中国科学技术大学学报,2006,5：550-555.
[160]洪文鹏,刘燕,周云龙.气液两相流流型图像信息熵递归特性分析[J].热能动力工程,2011,26(5)：538-542.
[161]周云龙,陈飞.水平气液两相流流型空间图像信息复杂性测度分析[J]化工学报,2008,59(1)：64-68.
[162]高忠科,金宁德等.多元时间序列复杂网络流型动力学分析[J].物理学报,2012,61(12),120510-120519.
[163]高忠科.两相流流型复杂网络非线性动力学特征研究[D].天津大学,2010.
[164]Sen A K, Longwic R, Litak G, et al. Analysis of cycle-to-cycle pressure oscillations in a diesel engine[J]. Mechanical Systems and Signal Processing,2008,22(2): 362-373.
[165]Hosmer D W, Lemeshow S. Applied logistic regression [M]. Wiley-Interscience, 2004.
[166]吕勇,徐金梧,李友荣.递归图和近似熵在设备故障信号复杂度分析中的应用[J].2006,机械强度,28(3)：317-321.
[167]Von Bloh W, Romano M C, Thiel M. Long-term predictability of mean daily temperature data[J]. Nonlinear Processes in Geophysics,2005,12(4):471-479.
[168]赵鹏,周云龙,孙斌.递归定量分析在离心泵故障诊断中的运用[J].振动、测试与诊断,2010,30(6)：612-617.
[169]汪小帆,李翔,陈关荣.复杂网络理论及其应用[M].清华大学出版社有限公司,2006.
[170]陆履亨.网络信息资源管理概论[M].上海人民出版社,2003.
[171]周涛,柏文洁,汪秉宏,等.复杂网络研究概述[J].物理,2005,34(01)：0.
[172]吴彤.复杂网络研究及其意义[J].哲学研究,2004(8)：58-63.
[173]郭雷,许晓鸣.复杂网络[M].上海科技教育出版社,2006.
[174]刘涛,陈忠,陈晓荣.复杂网络理论及其应用研究概述[J].系统工程,2005,6：000.
[175]孙惠泉.图论及其应用[M].科学出版社,2004.
[176]Erdos P, Renyi A. On the strength of connectedness of a random graph [J]. Acta Mathematica Hungarica,1961,12(1):261-267.
[177]杜海峰,李树茁,悦中山,等.小世界网络与无标度网络的社区结构研究[J].物理学报,2007,56(12)：6886-6893.
[178]Watts D J, Strogatz S H. Collective dynamics of'small-world'networks [J]. nature, 1998,393(6684):440-442.
[179]Barabasi A L, Albert R. Emergence of scaling in random networks [J]. science,1999, 286(5439):509-512.
[180]高自友,赵小梅,黄海军,等.复杂网络理论与城市交通系统复杂性问题的相关研究[J].交通运输系统工程与信息,2006,6(3)：41-47.
[181]方锦清.网络科学的理论模型探索及其进展[J].科技导报,2006,24(12)：67-72.
[182]吴金闪,狄增如.从统计物理学看复杂网络研究[J].物理学进展,2004,24(1)：18-46.
[183]Gang Y, Tao Z, Jie W, et al. Epidemic spread in weighted scale-free networks [J]. Chinese Physics Letters,2005,22(2):510.
[184]俞辉,王永骥,程磊.基于有向网络的智能群体群集运动控制[J].控制理论与应用,2007,24(1)：79-83.
[185]谭跃进,吴俊,邓宏钟.复杂网络中节点重要度评估的节点收缩方法[J].系统工程理论与实践,2006,26(11)：79-83.
[186]赫南,李德毅,淦文燕,等.复杂网络中重要性节点发掘综述[J].计算机科学,2007,34(12)：1-5.
[187]刘宏鲲,周涛.中国城市航空网络的实证研究与分析[J].物理学报,2007,56(1)：106-112.
[188]李季,汪秉宏,蒋品群,等.节点数加速增长的复杂网络生长模型[J].物理学报,2006,55(8)：4051-4057.
[189]杨博,刘大有,Jiming L, et al.复杂网络聚类方法[J].软件学报,2009,20(1)：54-66.
[190]Watts D J, Strogatz S H. Collective dynamics of'small-world'networks [J]. Nature, 1998,393(6684):440-442.
[191]张宇,张宏莉,方滨兴.Internet拓扑建模综述[J].软件学报,2004,15(8)：1220-1226.
[192]张培培,何阅,周涛,等.一个描述合作网络顶点度分布的模型[J].物理学报,2006,55(1)：60-67.
[193]杜海峰,李树茁,悦中山,等.小世界网络与无标度网络的社区结构研究[J].物理学报,2007,56(12)：6886-6893.
[194]Barabasi A L, Albert R. Emergence of scaling in random networks [J]. science,1999, 286(5439):509-512.
[195]车宏安,顾基发.无标度网络及其系统科学意义[J].系统工程理论与实践,2004,24(4)：11-16.
[196]Girvan M, Newman M E J. Community structure in social and biological networks [J]. Proceedings of the National Academy of Sciences,2002,99(12):7821-7826.
[197]Newman M E J, Girvan M. Finding and evaluating community structure in networks [J]. Physical review E,2004,69(2):026113.
[198]方锦清.非线性网络的动力学复杂性研究的若干进展[J].自然科学进展,2007,17(7)：841-857.
[199]李晓佳,张鹏,狄增如,等.复杂网络中的社团结构[J].复杂系统与复杂性科学,2008,5(3)：19-42.
[200]Hartigan J A, Wong M A. Algorithm AS 136:A k-means clustering algorithm[J]. Journal of the Royal Statistical Society. Series C (Applied Statistics),1979,28(1): 100-108.
[201]刘婷,胡宝清.基于聚类分析的复杂网络中的社团探测[J].复杂系统与复杂性科学,2007,4(1)：28-35.
[202]Zhong-Ke G, Ning-De J.两相流流型复杂网络社团结构及其统计特性[J].物理学报,2008,57(11)：6909-6920.
[203]Clauset A, Newman M E J, Moore C. Finding community structure in very large networks[J]. Physical review E,2004,70(6):066111.
[204]王立敏,高学东,宫雨,等.基于相对密度的社团结构探测算法[J].计算机工程,2009,35(1)：117-119.
[205]骆志刚,丁凡,蒋晓舟,等.复杂网络社团发现算法研究新进展[J].国防科技大学学报,2011,33(1)：47-52.
[206]Gao Z, Jin N. Complex network from time series based on phase space reconstruction [J]. Chaos:An interdisciplinary journal of nonlinear science,2009,19(3): 033137-033149.
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