网络混沌行为及其控制的研究
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摘要
网络中存在着大量的混沌行为,对网络混沌行为及其控制的研究有助于深入理解网络这个非线性动力系统的物理本质,以促进网络协议设计、业务量预测、网络规划以及网络性能分析等多个领域的发展。本文围绕网络中的混沌行为及混沌控制方法进行研究,侧重于流量的混沌特性及其控制,基于混沌理论的网络流量性能评估,TCP-RED禺散反馈系统中的混沌现象及其控制,以及网络中的混沌传播模型。论文的主要工作包括：
(1)深入分析了自相似流量时间序列和流量混沌吸引子的关系,并指出分形维数是联系流量自相似和混沌特征的纽带；同时,基于混沌理论提出了一种使用最大Lyapuno扌旨数对网络性能进行刻画的方法。
(2)提出了一种网络流量混沌控制方法。该方法基于混沌预测值对系统进行控制,将拥塞链路上呈现较强突发性的网络流量向指定的平衡点或区间进行引导,从而减小系统中的最大Lyapunov指数值,降低流量的突发强度。通过对实际网络流量的控制验证了该方法的有效性。
(3)研究了TCP-RED离散反馈系统中的边界碰撞分岔现象。通过范式方法分析了该TCP-RED系统中边界碰撞分岔的原因和种类,并根据不动点的稳定条件提出了一种混沌控制的方法,通过对不动点邻域内的状态变量进行扰动,将系统稳定在不动点,显著提高系统性能和资源利用率。仿真验证了该控制方法的有效性。
(4)讨论了网络中混沌现象的传播问题。建立了一个基于耦合映像格子的混沌传播模型,同时鉴于Internet的网络拓扑具有小世界特征且网络中节点的度服从幂率分布,故在本文中考虑了WS小世界网络和BA无标度网络两种典型的复杂网络拓扑结构。研究表明,若给定耦合强度,则在这两种网络中混沌节点数占总节点数的初始比例对最终的比例曲线均具有两个相变过程。仿真结果验证了分析结果。
There exist a large number of chaotic behaviors in network. The study of chaotic behavior and chaotic control on network can contribute to better understanding the physical nature of this nonlinear dynamical system, and therefore promote network protocol design, network traffic forecasting, network planning and network performance evaluation, etc. This dissertation makes an investigation into chaotic behavior and chaotic control on the network. It focuses on chaotic charactistics of network traffic and its chaotic control, performance evaluation of network traffic based on chaos theory, border collision bifurcation and chaotic control on discrete feedback TCP-RED system and propagation of chaos in network. The main contributions are as follows.
(1)The relationship between the self-similar time series of network traffic and the traffic chaotic attractor is analyzed in depth and it is pointed out that the fractal dimension is the association of the both; At the same time, a performance evalution method using the largest Lyapunov exponet based on chaos theory is proposed.
(2) A method of chaotic control on network traffic is presented. By this method, the chaotic network traffic can be controlled to pre-assigned equilibrium point according to chaotic prediction and the largest Lyapunov exponent (LLE) of the traffic on congested link is reduced, thereby the probability of traffic burst and network congestion can be reduced. Numerical examples show that this method is effective.
(3) Border collision bifurcations occurred in discrete feedback TCP-RED system is studied. The causes and types of the border collision bifurcations are analyzed based on the normal form method. And according to the linear stability condition of fixed point, a method of chaotic control is presented. With this method, the system can be stabilized to the fixed point by perturbing the state variable in the neighborhood of the fixed point. This method can significantly improve the performance and resource utilization of TCP-RED system, and simulation results show that it is effective.
(4) Propagation of chaos in the network is discussed. A dynamical model of chaos propagation based on coupled map lattices is established, meanwhile as the small-world characteristics of the Internet and the degree of network nodes obeys power-law distribution, the WS small-world network and BA scale-free network are considerd herein. The research suggests that in the two different networks, as the initial proportion of chaotic nodes increases, there are two phase change process of the final proportion of chaotic node for a given coupling strength. Numerical simulation results verify the theoretical analysis.
(1)深入分析了自相似流量时间序列和流量混沌吸引子的关系,并指出分形维数是联系流量自相似和混沌特征的纽带；同时,基于混沌理论提出了一种使用最大Lyapuno扌旨数对网络性能进行刻画的方法。
(2)提出了一种网络流量混沌控制方法。该方法基于混沌预测值对系统进行控制,将拥塞链路上呈现较强突发性的网络流量向指定的平衡点或区间进行引导,从而减小系统中的最大Lyapunov指数值,降低流量的突发强度。通过对实际网络流量的控制验证了该方法的有效性。
(3)研究了TCP-RED离散反馈系统中的边界碰撞分岔现象。通过范式方法分析了该TCP-RED系统中边界碰撞分岔的原因和种类,并根据不动点的稳定条件提出了一种混沌控制的方法,通过对不动点邻域内的状态变量进行扰动,将系统稳定在不动点,显著提高系统性能和资源利用率。仿真验证了该控制方法的有效性。
(4)讨论了网络中混沌现象的传播问题。建立了一个基于耦合映像格子的混沌传播模型,同时鉴于Internet的网络拓扑具有小世界特征且网络中节点的度服从幂率分布,故在本文中考虑了WS小世界网络和BA无标度网络两种典型的复杂网络拓扑结构。研究表明,若给定耦合强度,则在这两种网络中混沌节点数占总节点数的初始比例对最终的比例曲线均具有两个相变过程。仿真结果验证了分析结果。
There exist a large number of chaotic behaviors in network. The study of chaotic behavior and chaotic control on network can contribute to better understanding the physical nature of this nonlinear dynamical system, and therefore promote network protocol design, network traffic forecasting, network planning and network performance evaluation, etc. This dissertation makes an investigation into chaotic behavior and chaotic control on the network. It focuses on chaotic charactistics of network traffic and its chaotic control, performance evaluation of network traffic based on chaos theory, border collision bifurcation and chaotic control on discrete feedback TCP-RED system and propagation of chaos in network. The main contributions are as follows.
(1)The relationship between the self-similar time series of network traffic and the traffic chaotic attractor is analyzed in depth and it is pointed out that the fractal dimension is the association of the both; At the same time, a performance evalution method using the largest Lyapunov exponet based on chaos theory is proposed.
(2) A method of chaotic control on network traffic is presented. By this method, the chaotic network traffic can be controlled to pre-assigned equilibrium point according to chaotic prediction and the largest Lyapunov exponent (LLE) of the traffic on congested link is reduced, thereby the probability of traffic burst and network congestion can be reduced. Numerical examples show that this method is effective.
(3) Border collision bifurcations occurred in discrete feedback TCP-RED system is studied. The causes and types of the border collision bifurcations are analyzed based on the normal form method. And according to the linear stability condition of fixed point, a method of chaotic control is presented. With this method, the system can be stabilized to the fixed point by perturbing the state variable in the neighborhood of the fixed point. This method can significantly improve the performance and resource utilization of TCP-RED system, and simulation results show that it is effective.
(4) Propagation of chaos in the network is discussed. A dynamical model of chaos propagation based on coupled map lattices is established, meanwhile as the small-world characteristics of the Internet and the degree of network nodes obeys power-law distribution, the WS small-world network and BA scale-free network are considerd herein. The research suggests that in the two different networks, as the initial proportion of chaotic nodes increases, there are two phase change process of the final proportion of chaotic node for a given coupling strength. Numerical simulation results verify the theoretical analysis.
引文
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