论类洛伦兹混沌系统的全局指数吸引集及应用

Globally exponentially sets of Lorenz-like system and its application

通过构造广义正定径向无界的Lyapunov函数和最优化理论,研究了一个在现实中有实际应用背景的三维类洛伦兹系统的全局指数吸引集和正向不变集,得到了三维椭球估计,然后将得到的x,y,z的界应用到混沌同步中,设计一个尽可能简单的线性控制器研究了该系统的完全同步。数值仿真验证了同步理论的有效性。

The globally exponentially and positively invariant sets of one chaotic system are investigated via constructing a positively definite and radically unbounded Lyapunov function and optimization theory.For the system,it derives three-dimensional ellipsoidal ultimate bound.The result is applied to the chaos synchronization.Numerical simulations are presented to show the effectiveness of the proposed scheme.