基于忆阻器的Sprott-B超混沌系统的动力学分析与电路实现

Dynamics analysis and circuit realization of Sprott-B hyper-chaotic system based on memristor

将二次型磁控忆阻器引入混沌系统,构建了一个新的四阶超混沌忆阻系统。首先探讨了忆阻系统的特性,采用包括Lyapunov指数和维数、耗散性、无限多平衡点集与稳定性等的分析方法,确定了新忆阻系统的超混沌特性,得到了无尽的平衡点集,与原系统对比发现新系统更复杂,混沌程度更高。进而研究了新系统的动力学行为,观察到随系统参数不同引起的瞬态混沌现象和随初始值不同引起的吸引子共存等现象,这是首次对包含常数项的混沌系统做出的动力学分析。最后设计并搭建了该系统的模拟电子电路,实验表明示波器结果与数值仿真结果具有良好的一致性,为忆阻超混沌系统的实际应用奠定了基础。

A new fourth order hyperchaotic memristor system is constructed by introducing a magnetron memristor into the chaotic system.Firstly,the characteristics of the memristor system are discussed.The hyperchaotic characteristics of the new memristor system are determined by using analysis methods including Lyapunov exponent and dimension,dissipation,infinite multiple equilibrium sets and stability,and the infinite equilibrium sets are obtained.Compared with the original system,it is found that the new system is more complex and more chaotic.Secondly,the dynamic behavior of the new system is investigated,and the transient chaos caused by different parameters and the co-existence of attractors caused by different initial values are observed.This is the first analysis of this phenomenon for a system containing constant.Finally,the simulation electronic circuit of the system is designed and built.The experimental results show that the oscilloscope results are consistent with the numerical simulation results,which provides a basis for the practical application of the memristor hyperchaotic system.