一种具有超级多稳态的忆阻混沌系统及其在电力图像加密中的应用  

A Memristive Chaotic System with Extreme Multistability and Its Application in Power Image Encryption

作　　者：邓迎军 荣海媚 周钦君 孙智鹏 张博 Deng Yingjun;Rong Haimei;Zhou Qinjun;Sun Zhipeng;Zhang Bo(State Grid Jingzhou Electric Power Supply Company,Jinzhou,Hubei 434099,China;Enshi Vocational and Technical College,Enshi,Hubei 445000,China;College of Intelligent Systems Science and Engineering,Hubei Minzu University,Enshi,Hubei 445000,China)

机构地区：[1]国网湖北省电力有限公司荆州供电公司,湖北荆州434099 [2]恩施职业技术学院,湖北恩施445000 [3]湖北民族大学智能科学与工程学院,湖北恩施445000

出　　处：《机电工程技术》2024年第8期191-196,共6页Mechanical & Electrical Engineering Technology

基　　金：国网荆州供电公司科技计划项目(B715J0230019)。

摘　　要：混沌系统的构造和图像加密是相互联系、相互独立的研究方向,同时也是当前混沌系统的研究热点。在Sprott-I混沌系统中引入绝对值忆阻器,构造了一个新的忆阻混沌系统。受忆阻器强非线性的影响,新系统的平衡点变为了一条线平衡点集,表现出了更丰富的动力学特性。通过MATLAB仿真分析了该系统的Lyapunov指数、耗散性、分岔图等动力学特征,结果表明新系统不但能产生依赖系统参数变化的混沌吸引子和周期极限环的常规现象,而且能够产生恒Lyapunov指数以及依赖于初始条件变化的分岔图偏移以及无限多吸引子共存的超级多稳态的特殊动力学现象。最后,考虑到系统在引入忆阻器后出现的超级多稳态现象,能够产生鲁棒性更好的伪随机序列,因此将该系统和DNA编码结合引入到电力图像加密中,在MATLAB平台上进行安全分析实验结果表明,该算法具有良好的加密效果。It is an interrelated and independent research direction for the construction of chaotic systems and image encryption,and also the current research hotspot of chaotic systems.A new memristive chaotic system is constructed by introducing an absolute value memristor into the Sprott-I chaotic system.Affected by strong nonlinearity of the memristor,the equilibrium points of the new system become a line equilibrium set,showing richer dynamic characteristics.The dynamic characteristics of the system,such as Lyapunov exponent,dissipation and bifurcation diagram,are analyzed by MATLAB simulation.The results show that the new system can not only produce the conventional phenomena of chaotic attractors and periodic limit cycles depending on the change of system parameters,but also produce the special dynamic phenomena of constant Lyapunov exponent,bifurcation diagram shift depending on the change of initial conditions and super multi-stable state with infinite attractors.Finally,considering the super multi-stability phenomenon of the system after the introduction of the memristor,it can generate more robust pseudo-random sequences.Therefore,the system and DNA coding are introduced into the power image encryption.The security analysis experimental results on the MATLAB platform show that the algorithm has a good encryption effect.

关 键 词：超级多稳态 恒Lyapunov指数 平衡点稳定性 忆阻混沌系统 图像加密 

分 类 号：TN911.73[电子电信—通信与信息系统]