多涡卷混沌吸引子同步的双控制器

Double-controller of synchronizing chaotic systems with multi-scroll attractors

针对驱动系统与响应系统不同混沌状态的同步问题,提出了一种双控制器控制方法。依据Lyapunov稳定性理论,对两系统同步误差的稳定性进行了分析和证明,并对5涡卷与3涡卷、5涡卷与非混沌态Chua电路之间的同步进行了计算机数值仿真实验。结果表明,不受初始条件和参数差的限制,只要驱动系统是混沌状态,无论响应系统是混沌态还是非混沌态,该控制器都能有效地控制同步,并误差图和时序图显示出了双控制器可在2s内控制不同涡卷吸引子系统同步,在5s内能控制非混沌态的系统与混沌系统同步。

To solve synchronization problems of different chaotic states in driving system and driven system, a double-controller control method is presented. According to Lyapunov stability theory, the synchronization error of two chaotic systems was analyzed and proved to be asymptotically stabile, and the synchronization between 5-scroll and 3-scroll Chua＇s circuits, and 5-scroll and non-chaos Chua＇s circuits were studied by computer simulation experiments. The experimental results demonstrate that the double-controller can effectively control the synchronization of two systems if only the driving system is chaos state without the limit of initial conditions and parameter errors. At the same time errors vs. time and time evolution of synchronization process show that the double controller can synchronize between different scroll attractor circuits within 2 seconds, and between chaos circuit and non-chaos circuit within 5 seconds.