含多吸引子的忆阻混沌系统的分析与实现  

Analysis and implementation of memristive chaotic system with multiple attractors

作　　者：曹可 赖强 赖聪 CAO Ke;LAI Qiang;LAI Cong(School of Electrical and Automation Engineering,East China Jiaotong University,Nanchang 330013,Jiangxi Province,P.R.China)

机构地区：[1]华东交通大学电气与自动化工程学院,江西南昌330013

出　　处：《深圳大学学报（理工版）》2022年第4期480-488,共9页Journal of Shenzhen University(Science and Engineering)

基　　金：国家自然科学基金资助项目(61961019)。

摘　　要：采用磁控忆阻器作为Sprott-J系统的负反馈,构造了一个新的具有无限平衡点的4维忆阻混沌系统,将所有的非线性项都集中在一个方程中.分析系统的耗散性、平衡点集的存在性和稳定性,以及Lyapunov指数和维数,利用分岔图和Lyapunov指数谱观察并研究该混沌系统的动力学特征.Matlab数值仿真结果表明,新系统是耗散系统且具有1个线平衡点集.动力学分析结果表明,新忆阻Sprott-J系统在改变参数时存在反倍周期分岔现象,改变初始条件时,系统出现多吸引子共存现象.研究系统在不同初始条件和系统参数下的分岔特性,得到系统混沌与混沌、混沌与周期、周期与周期共存的多吸引子特性.采用Multisim软件对系统进行电路模拟及数值仿真,结果表明,数值仿真结果与相应的电路结果相吻合,验证了新忆阻Sprott-J混沌系统的物理可行性.研究为忆阻Sprott-J混沌系统在图像加密领域的应用提供了理论基础.A new four-dimensional memristive chaotic system with infinite equilibrium points is constructed by introducing the magnetically controlled memristor as the negative feedback of Sprott-J system.All non-linear terms of the system are concentrated in a single equation.The dissipation of the system,the existence and stability of the equilibrium point set and the Lyapunov exponent and dimension of the system are analyzed.The dynamic characteristics of the chaotic system are studied by using bifurcation diagram and Lyapunov exponent spectrum.The numerical simulation of Matlab show that the new system is a dissipative system and has a set of line equilibrium points.The dynamic analysis results show that the new memristive Sprott-J system has the phenomenon of inverse period-doubling bifurcation when changing the parameters,and the coexistence of multiple attractors when changing the initial conditions.The chaotic bifurcation characteristics of the system under different initial conditions and system parameters are studied.The multiple attractor characteristics of chaos and chaos,chaos and period,period and period coexistence are obtained.The circuit implementation and numerical simulation of the system are carried out by using Multisim software.The results show that the numerical simulation is consistent with the corresponding circuit results,which verifies the physical feasibility of the new memristive Sprott-J chaotic system,and provides a theoretical basis for the application of the system in the field of image encryption.

关 键 词：混沌 忆阻Sprott-J混沌系统 反倍周期分岔 多吸引子 分岔图 LYAPUNOV指数谱 电路实现 

分 类 号：TM132[电气工程—电工理论与新技术] O415.5[理学—理论物理]