有源荷控忆阻系统的多稳态分析及电路实现

采用有源荷控忆阻替换蔡氏电路中的非线性电阻,实现一个五维忆阻非线性电路系统. 建立了该系统的无量纲方程,分析了系统的平衡点集与稳定性. 利用分岔图、Lyapunov指数谱和相轨迹图等分析方法,从多角度研究了随系统参数与初始状态变化而产生的多稳态动力学行为. 研究表明,当系统参数、初始状态变化时,都会出现不同拓扑结构的混沌吸引子共存、不同吸引域的多周期极限环共存、不同周期数的极限环与不同拓扑结构的混沌吸引子等共存行为. 最后,设计了五维忆阻混沌系统的模拟电路模型,电路仿真实验与数值仿真结果相一致,观测到不同的多稳态共存运动. 这表明动力学分析的正确性和系统的物理可实现性,为进一步拓展系统加密应用奠定基础.

Multi-Stability Analysis of an Active Charge-ControlledMemristive System and Circuit Implementation

In the paper,a new type of five-dimensional memristive chaotic system is easily implemented by replacing a nonlinear resistance in the Chua’s circuit with an active charge-controlled memristor. Firstly,the stable equilibrium and unstable equilibrium point sets of the system are analyzed theoretically by establishing the dimensionless equation. Next,through Lyapunov index spectrum,bifurcation diagram and phase track diagram,the coexistence phenomena of the system with respect to the changes and initial condition is studied. When different initial conditions are used,the system displays the coexistent phenomenon of chaotic attractors with different topological structures or several limit cycles with different attraction domains,as well as the phenomenon of multiple attractors of several periodic limit cycle and chaotic attractors with multiple topological structures. Finally,based on multisim circuit simulation model,the simulation results are consistent with the numerical simulations and relevant theoretical analysis. These show the correctness of dynamic analysis and the physical realizability of the system,and lay a foundation for expanding the application in encryption.