N-涡卷超混沌吸引子产生与同步的研究

Study on Generation and Synchronization of N-Scroll Hyperchaotic Attractors

四阶MCK电路的主要特点是产生双涡卷超混沌吸引子 .本文提出在该电路中产生N 涡卷超混沌吸引子的一种新方法 .构造一个具有 2N - 1个分段线性的奇函数 ,其构造方法是使该函数中的每一个平衡点分别位于相邻两个转折点的正中间 ,并保持混沌吸引子中涡卷与键带的相互间置 ,在此基础上利用递推的方法求得该函数中的各个递推参数 ,从而可在MCK电路中产生N 涡卷超混沌吸引子 .基于李雅普诺夫稳定性理论 ,研究了两个N 涡卷超混沌吸引子的单向耦合同步问题 .最后给出了N 涡卷超混沌吸引子产生及其同步的计算机数值模拟结果 .

The feature of the MCK circuit is that it can generate double-scroll hyperchaotic attractor. This paper presents a new approach for generating N-scroll hyperchaotic attractors in the MCK circuit. A 2N-1-segment piecewise-linear odd function is constructed in the presented scheme. The construction method is used to make each equilibrium point located in the center of two adjacent breakpoints, and keep scrolls and bond orbits alternated with each other. Using the recurrence formula, the recurrence parameters of the 2N-1-segment piecewise-linear odd function can be determined so as to obtain N-scroll hyperchaotic attractors. Based on Lyapunov stability theory, the synchronization of N-scroll hyperchaotic attractors is studied. Finally, the results of generation and synchronization of N-scroll hyperchaotic attractors are given.