忆阻Sprott-R混沌系统的复杂动态分析与电路实现

Complex dynamic analysis and circuit realization of memristive Sprott⁃R chaotic system

基于Sprott-R三维混沌系统,提出了一个具有多稳态和调幅特性的简单四维忆阻混沌系统。首先分析了系统的稳定性,发现该系统具有无穷多个不稳定平衡点。进而利用Lyapunov指数谱、分岔图及相平面图,研究了该忆阻混沌系统的复杂动力学行为特性。研究结果表明,当系统参数发生变化时,系统会经反倍周期分岔由混沌态进入周期态;在不同初始条件下,系统能产生三种共存吸引子,分别为双混沌吸引子共存、周期极限环与混沌吸引子共存、双周期极限环共存;当初始条件变化时,系统输出四维混沌信号的幅度均发生变化。最后,对该系统进行了电路设计与仿真,验证了该忆阻混沌系统的存在性。

A simple four-dimensional memristive chaotic system with multistability and amplitude modulation characteristics is constructed based on three-dimensional Sprott-R chaotic system.Firstly,the system's stability characteristics are analyzed,and it is found that the system has infinite unstable equilibrium points.And then,the complex dynamical behaviors of the memristive chaotic system are studied using Lyapunov exponential spectrum,bifurcation diagram and the projection of chaotic attractors on the phase plane.The results show that when the system parameters change,the system will change from chaotic state to periodic state through inverse periodic bifurcation.And under different initial conditions,the system can generate three kinds of coexistence attractors,namely chaotic attractors coexistence,periodic limit cycle and chaotic attractor coexistence,and periodic limit cycles coexistence.In addtion,when the initial conditions change,the amplitude of the four-dimensional chaotic signals will change.Finally,the circuit design and realization of the system are carried out to further verify the existence of the new system.