分数阶Lorenz超混沌系统的动力学分析与电路设计

针对一类分数阶Lorenz超混沌系统,分别从系统的分岔图、Lyapunov指数图和吸引子相图等角度分析与验证了分数阶Lorenz超混沌系统丰富的动力学行为.同时基于整数阶混沌电路的设计策略,设计了模拟电路,实现了分数阶Lorenz超混沌系统.最后,通过示波器观察到电路仿真结果与数值仿真结果具有一致性,从而揭示了分数阶超混沌系统的可实现性,也表明了分数阶混沌电路的正确性.

Dynamics Analysis and Circuit Implementation for the Fractional-order Lorenz Hyperchaotic System

This paper,for a fractional order Lorenz hyperchaotic system,is to analyze and verify the fractional order Lorenz hyperchaotic system dynamics behavior based on such numerical simulations as the bifurcation diagram,the Lyapunov index figure and attractor phase diagram.The analog circuit was designed and the fractional order Lorenz chaotic system is realized on the basis of integer order chaotic circuit design strategy.Finally,the consistence of numerical simulation results and circuit simulation results observed through the oscilloscope reveals the realizability of hyperchaotic system of fractional order,and the validity of the fractional order chaotic circuit.