Analyzing of Hopf Bifurcation Based on Deterministic Learning
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- 英文论文题名：Analyzing of Hopf Bifurcation Based on Deterministic Learning
- 论文作者：Danfeng Chen ; Peng Lin ; Cong Wang
- 英文论文作者：Danfeng Chen ; Peng Lin ; Cong Wang ; School of Automation ; Foshan University ; School of Automation Science and Engineering ; South China University of Technology
- 年：2017
- 作者机构：School of Automation,Foshan University;School of Automation Science and Engineering,South China University of Technology;
- 英文论文关键词：system identification ; Hopf bifurcation ; deterministic learning ; nonlinear dynamics ; structure stability ; HH model
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O19
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：405k
- 原文格式：D
- 会议级别：全国
摘要
For parameter dependent nonlinear system, once the parameter reaches a critical point, the equivalent relationship of the system trajectory will be destroyed and further lead to structural instability of the whole system. This is the dynamic bifurcation phenomenon and is also the fundamental cause of instability oscillations and dynamic failures for most practical systems.In this research, Hopf bifurcation, the most common and typical dynamic bifurcation, will be discussed through deterministic learning theory. Firstly, an algebraic criterion of Hopf bifurcation is proposed according to the classical Hurwitz criterion, which provides a more convenient tool for Hopf bifurcation analyzing. Then, the bifurcation process with the change of system dynamics due to abnormal parameter variation is analyzed through deterministic learning. A C~1-norm based measure and negative exponential dynamic index are presented according to the structural stability theory, which can be used to analyze the steady state of current system. Finally, the classical Hodgkin-Hexley model is introduced to verify the feasibility and validity of the proposed algorithm.
For parameter dependent nonlinear system, once the parameter reaches a critical point, the equivalent relationship of the system trajectory will be destroyed and further lead to structural instability of the whole system. This is the dynamic bifurcation phenomenon and is also the fundamental cause of instability oscillations and dynamic failures for most practical systems.In this research, Hopf bifurcation, the most common and typical dynamic bifurcation, will be discussed through deterministic learning theory. Firstly, an algebraic criterion of Hopf bifurcation is proposed according to the classical Hurwitz criterion, which provides a more convenient tool for Hopf bifurcation analyzing. Then, the bifurcation process with the change of system dynamics due to abnormal parameter variation is analyzed through deterministic learning. A C~1-norm based measure and negative exponential dynamic index are presented according to the structural stability theory, which can be used to analyze the steady state of current system. Finally, the classical Hodgkin-Hexley model is introduced to verify the feasibility and validity of the proposed algorithm.
For parameter dependent nonlinear system, once the parameter reaches a critical point, the equivalent relationship of the system trajectory will be destroyed and further lead to structural instability of the whole system. This is the dynamic bifurcation phenomenon and is also the fundamental cause of instability oscillations and dynamic failures for most practical systems.In this research, Hopf bifurcation, the most common and typical dynamic bifurcation, will be discussed through deterministic learning theory. Firstly, an algebraic criterion of Hopf bifurcation is proposed according to the classical Hurwitz criterion, which provides a more convenient tool for Hopf bifurcation analyzing. Then, the bifurcation process with the change of system dynamics due to abnormal parameter variation is analyzed through deterministic learning. A C~1-norm based measure and negative exponential dynamic index are presented according to the structural stability theory, which can be used to analyze the steady state of current system. Finally, the classical Hodgkin-Hexley model is introduced to verify the feasibility and validity of the proposed algorithm.
引文
[1]C.W.Tan,M.Varghese,P.Varaiya,Bifurcation and chaos in power systems,Sdhan,1993,18(5):761-786.
[2]L.Yang,X.Ma,Analysis on voltage stability of power system with doubly fed induction generator wind turbine based on bifurcation theory,Transactions of China Electrotechnical Society,2012,27(9):1-8.
[3]A.Duval,C.Loty,Ionic currents in mammalian fast skeletal muscle,Journal of Physiology,1978,278(1):403-423.
[4]D.W.Berns,J.L.Moiola,G.Chen,A quasi-analytical method for period-doubling bifurcation,IEEE International Symposium on Circuits and Systems,2001(2):739-742.
[5]P.A.Pappone,Voltage-clamp experiments in normal and denervated mammalian skeletal muscle fibres,Journal of Physiology,1980,306(1):377.
[6]Y.Yu,H.X.Li,S.Wang,Dynamic analysis of a fractionalorder Lorenz chaotic system,Chaos Solitons and Fractals,2009,42(2):1181-1189.
[7]W.Du,J.Yu,J.Zhang,et al,An analysis of Hopf bifurcation for an autonomous chaotic system.2013,37(5).
[8]N.S.Namachchivaya,S.T.Ariaratnam,Periodically perturbed Hopf bifurcation,Siam Journal on Applied Mathematics,1987,47(1):15-39.
[9]A.L.Hodgkin,A.F.Huxley,A quantitative description of membrane current and its application to conduction and excitation in nerve,Bulletin of Mathematical Biology,1990,117(1):500-544.
[10]J.Aweya,M.Ouellette,D.Y.Montuno,Design and stability analysis of a rate control algorithm using the Routh-Hurwitz stability criterion,IEEE/ACM Transactions on Networking,2004,12(4):719-732.
[11]C.Wang,D.J.Hill,Learning from neural control,IEEE Transactions on Neural Networks,2006,17(1):130-146.
[12]D.F.Chen,C.Wang,Prediction of Period-Doubling Bifurcation Based on Dynamic Recognition and Its Application to Power Systems,International Journal of Bifurcation and Chaos,2016,26(09).
[13]D.Chen,C.Wang,X.Dong,Modeling of nonlinear dynamical systems based on deterministic learning and structural stability,Science China Information Sciences,2016(9):1-16.
[14]M.Stuchly,T.W.Dawson,Interaction of low-frequency electric and magnetic fields with the human body,Proceedings of the IEEE,2000,88(5):643-664.
[15]J.Guckenheimer,S.Gueron,R.M.Harris-Warrick,Mapping the dynamics of a bursting neuron,Philosophical Transactions of the Royal Society of London,1993,341(1298):345-359.
[2]L.Yang,X.Ma,Analysis on voltage stability of power system with doubly fed induction generator wind turbine based on bifurcation theory,Transactions of China Electrotechnical Society,2012,27(9):1-8.
[3]A.Duval,C.Loty,Ionic currents in mammalian fast skeletal muscle,Journal of Physiology,1978,278(1):403-423.
[4]D.W.Berns,J.L.Moiola,G.Chen,A quasi-analytical method for period-doubling bifurcation,IEEE International Symposium on Circuits and Systems,2001(2):739-742.
[5]P.A.Pappone,Voltage-clamp experiments in normal and denervated mammalian skeletal muscle fibres,Journal of Physiology,1980,306(1):377.
[6]Y.Yu,H.X.Li,S.Wang,Dynamic analysis of a fractionalorder Lorenz chaotic system,Chaos Solitons and Fractals,2009,42(2):1181-1189.
[7]W.Du,J.Yu,J.Zhang,et al,An analysis of Hopf bifurcation for an autonomous chaotic system.2013,37(5).
[8]N.S.Namachchivaya,S.T.Ariaratnam,Periodically perturbed Hopf bifurcation,Siam Journal on Applied Mathematics,1987,47(1):15-39.
[9]A.L.Hodgkin,A.F.Huxley,A quantitative description of membrane current and its application to conduction and excitation in nerve,Bulletin of Mathematical Biology,1990,117(1):500-544.
[10]J.Aweya,M.Ouellette,D.Y.Montuno,Design and stability analysis of a rate control algorithm using the Routh-Hurwitz stability criterion,IEEE/ACM Transactions on Networking,2004,12(4):719-732.
[11]C.Wang,D.J.Hill,Learning from neural control,IEEE Transactions on Neural Networks,2006,17(1):130-146.
[12]D.F.Chen,C.Wang,Prediction of Period-Doubling Bifurcation Based on Dynamic Recognition and Its Application to Power Systems,International Journal of Bifurcation and Chaos,2016,26(09).
[13]D.Chen,C.Wang,X.Dong,Modeling of nonlinear dynamical systems based on deterministic learning and structural stability,Science China Information Sciences,2016(9):1-16.
[14]M.Stuchly,T.W.Dawson,Interaction of low-frequency electric and magnetic fields with the human body,Proceedings of the IEEE,2000,88(5):643-664.
[15]J.Guckenheimer,S.Gueron,R.M.Harris-Warrick,Mapping the dynamics of a bursting neuron,Philosophical Transactions of the Royal Society of London,1993,341(1298):345-359.