Panchev系统的全局指数吸引集及其应用

摘要

通过构造广义正定径向无界的Lyapunov函数,研究了一个包含三维Lorenz系统在内的Panchev系统的全局指数吸引集和正向不变集,得到了三维圆柱估计,并用数值仿真验证了三维圆柱估计式的有效性.然后利用一个非线性控制器将得到的全局指数吸引集的结果应用到混沌同步中,研究了该系统的全局指数同步问题.%Constructing a positive definite and radial unbounded Lyapunov function, we obtain the global exponential attractive set and the positive invariant set of Panchev system containing a 3-dimensional Lorenz system. On this basis, we obtain the 3-dimensional cylindrical ultimate bound which is validated numerically. Finally, the global exponential attractive set obtained from a nonlinear controller is applied to the synchronization of a chaotic system, and its global exponential synchronization problem is investigated.