一类具有忆阻器的Lorenz 型混沌系统稳定性及余维一分岔分析

Stability and Co-Dimension One Bifurcation Analysis of a Class of Lorenz-Type Chaotic System with Memristor

基于经典的Lorenz 系统,本文通过反馈控制的方式得到了一类具有忆阻器的三维混沌电路系统,并对该系统的局部动力学行为进行了分析。首先,通过分析线性化系统,得到了原点平衡点的局部稳定性性质;其次,基于中心流形及Hopf 分岔理论,对原点平衡点处的余维一Pitchfork 分岔及Hopf 分岔进行了分析,并通过数值仿真进行了验证。

Based on the classical Lorenz system,this paper obtains a class of 3D memristive chaotic circuit system through feedback control,and analyzes the local dynamics of this system.Firstly,the local stability at the origin of this system is investigated through analyzing linearized system.Secondly,based on the center manifold theorem and Hopf bifurcation theory,the co-dimension one Pitchfork bifurcation and Hopf bifurcation at the origin of this system are investigated,and the results are veri?ed by numerical simulation.