Research On Chaotic Behavior And Chaotic Control Of Networks

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.