基于反馈法的混沌系统反控制及其应用研究

Bifurcation phenomena and chaotic behvior in a two-dimensional delayed nonlinear neural network model, which can be viewed as an anticontrol chaos generator, are investigated by making use of eigenvalue and eigenvector analysis method and numerical simulations. Local bifurcations for an one-dimensional nonlinear delayed feedback chaos anticontrol system are explored and Hopf bifurcations occurring around many equilibria and thus resulting in the complex behavior of the system are proved and observed. Based on a delayed feedback chaos anticontrol system, a novel chaotic phase shift keying secure communication system is proposed, in which two schemes are implemented, one is based on observer theory and uses a linear combination of the system state variables as the transmitting signal, while another uses a nonlinear function of the state variables. Such chaotic secure communication system has advantages of controllable synchronization speed, strong chaotic signal and simple structure. Using the Lyapunov function and functional approaches, global and exponential stabilities for delayed neural networks are studied and some sufficient criteria are derived, which unify and generalize some existing results and can be applied to the design of neural networks.

利用反馈控制的理论和方法，研究混沌系统控制的反问题：混沌反控制问题。即通过反馈法，使非混沌系统变为混沌的，并具有期望的数值特性以及统计特性。采用线性和非线性反馈、时延反馈及外力反馈等多种方法进行反控制。受控的混沌系统可作为混沌发生器，研究受控的混沌发生器在优化和保密通信方面的应用。理论和应用研究达到国际领先水平。