一类忆阻型4D保守混沌系统的设计及其分析

Design and analysis of a 4D conservative chaotic system based on memristors

提出一类基于忆阻器、具有非双曲平衡点的非哈密顿四维保守混沌系统。通过计算系统的散度,分析了系统相体积的守恒性;对系统进行Kolmogorov变换,证明了系统哈密顿能量并不守恒;同时该系统对参数和初始值变化敏感。运用系统的相轨图、Lyapunov指数谱、Poincaré映射、分岔图等理论和数值分析工具,分析了系统复杂的动力学行为,得知系统具有混沌流与不同幅度准周期流的非对称共存等多稳态特性;最后,通过模拟电路验证了设计的可行性与分析的正确性。该保守系统具有良好的初始值灵敏性,可应用在信息和图像加密等领域。

A non-Hamiltonian 4D conservative chaotic system was proposed with non-hyperbolic equilibrium point based on memristors.The conservatism of the phase volume of the system was analyzed by calculating the divergence of the system.The Kolmogorov transformation of the system proves that the Hamiltonian energy of the system is not conservative.And the system is sensitive to the variation of parameters and initial values.The complex dynamic behaviors of the system were analyzed by using theoretical and numerical analysis tools such as Lyapunov exponent spectrum,Poincarémap,and bifurcation diagram.The system has the characteristics of multi-stable state,such as asymmetric coexistence between chaotic flow and quasi periodic flow of different amplitudes.Finally,the feasibility of the design and the correctness of the analysis were verified by the analog circuit.With good sensitivity to initial values,the conservative system can be used in information and image encryption fields.