一个切换Lorenz混沌系统的特性分析

为使混沌系统更好地应用于工程实践,通过构造由2个子系统组成的切换Lorenz型混沌系统,分析子混沌系统和自动切换混沌系统的Lyapunov指数谱和分岔图,利用拓扑马蹄引理从理论上证明了切换混沌系统吸引子的存在性,基于模拟电路和数字电路2种实验手段实现了混沌系统,分析结果表明,在相同参数下,切换系统具有与子系统的不同的动力学特性,切换系统比子系统具有更大的混沌参数区间.实验结果与仿真结果完全一致,在理论和实验两方面证明了切换混沌系统的存在性.

Analysis of properties of a switched Lorenz type chaotic system

In order to promote the application of chaotic systems in engineering practice, this paper presents a Lorenz-type switched system composed of two subsystems. The new chaotic system is analyzed with Lyapunov exponent spectrum and bifurcation diagram. To present a computer assisted verification of chaos, the switching system is also studied by utilizing topological horseshoe theory. Physical verification has also been done in two different methods with an analog electronic circuit and a digital electronic circuit, respectively. Numerical analysis shows that the switched system has a larger chaotic region than its subsystems and the dynamics characteristics much different from subsystems. It also shows that numerical and experimental results are matches very well. The existence of the chaotic attractors is proved in both theory and experiment.