呈现超级多稳态忆阻系统的动力学与实现

Dynamics and Implementation of Memristive System Exhibiting Extreme Multistability

在一类参数可调的混沌系统的基础上,用忆阻器替换原系统电路的增益电阻,建立改进型四维忆阻混沌系统。理论分析显示,新系统具有两个线平衡点且能产生自激吸引子。通过分岔图、李雅普诺夫指数谱和相轨图等数值仿真手段分析新系统的动力学,发现随着初始条件的变化,参数固定的忆阻系统不仅存在无穷多吸引子共存的超级多稳态现象,还存在复杂的暂态行为。最后,设计忆阻系统的等效电路,硬件电路实验和PSIM电路仿真验证了数值仿真的正确性。

Based on a class of parameter-adjustable chaotic systems,an improved four-dimensional memristive chaotic system is established by replacing the gain resistor of the original system circuit with a memristor.Theoretical analysis demonstrates that the new system possesses two line equilibrium points and can generate self-excited attractors.The dynamics of the new system are analyzed through numerical simulation such as bifurcation diagrams,Lyapunov exponents,phase diagrams,etc.With the variation of initial conditions,the memristive system with fixed parameters exhibits not only the extreme multistability phenomenon of coexisting infinitely many attractors but also complex transient behaviors.Finally,to validate the theoretical and numerical simulation results,an equivalent circuit of the memristive chaotic system is designed,and hardware circuit experiments as well as PSIM circuit simulations confirm the correctness of the MATLAB numerical simulations.