忆阻Lorenz混沌系统的动力学分析与电路实现  

Dynamics Analysis and Circuit Implementation of the Memristive Lorenz Chaotic System

作　　者：赵双 陈湘军 张云贞 ZHAO Shuang;CHEN Xiangjun;ZHANG Yunzhen(School of Software and Big Data,Changzhou College of Information Technology,Changzhou,Jiangsu 213164,China;School of Information Engineering,Xuchang University,Xuchang,Henan 461000,China)

机构地区：[1]常州信息职业技术学院软件与大数据学院,江苏常州213164 [2]许昌学院信息工程学院,河南许昌461000

出　　处：《计算物理》2024年第2期268-276,共9页Chinese Journal of Computational Physics

基　　金：中国高校产学研创新基金(2021FNB02003);河南省高等学校重点科研项目(21A120007);河南省自然科学基金(202300410351);常州信息职业技术学院科研课题(CXZK202006Y)资助项目。

摘　　要：基于所提的一类光滑二次通用忆阻器,构建一种忆阻Lorenz混沌系统。稳定性分析表明,系统具有与原系统相同的平衡点和稳定性,即一个不稳定鞍点和两个不稳定鞍焦。利用分岔图、李雅普诺夫指数谱、相图等分析方法揭示所提忆阻系统的动力学,结果表明:忆阻Lorenz混沌系统具有共存双稳态模式和自相似分岔结构。最后,通过改变通用忆阻器的内部参数实现对系统的幅度调控,分别设计忆阻器和忆阻系统等效电路并利用模拟元件综合,仿真结果证实了数值模拟的正确性。Memristor plays an important role in modeling nonlinear circuits and systems.Based on the proposed smooth quadratic generic memristor,this paper proposes a memristor-based Lorenz chaotic system.Different from the chaotic system on account of memristor feedback,this system takes a variable of the original Lorenz chaotic system as an inner state variable of memristor,so as to ensure that the system dimension does not increase.Stability analysis shows that the system has the same equilibrium point and stability as the original Lorenz system,namely,one unstable saddle point and two unstable saddle foci.By means of bifurcation diagram,Lyapunov exponent spectra,and phase plot,the dynamics of the proposed memristive system are revealed.The simulated results show that the memristive Lorenz chaotic system possesses coexisting bistable mode and self-similar bifurcation structures.What is more interesting is that the amplitude of the system can be regulated by changing the inner parameters of the generic memristor.Finally,the equivalent circuits of memristor and memristive system are designed and also synthesized by analog components.Simulation results confirm the correctness of the numerical simulations.

关 键 词：通用忆阻器 混沌动力学 LORENZ混沌系统 双稳态 电路实现 

分 类 号：O415.5[理学—理论物理]