ABSTRACT

Asymmetric property of the pinched hysteresis loop usually appears in a real memristor. To imitate this property, an asymmetric memristor emulator is constructed by an analog circuit consisting of a non-balance diode-bridge and a resistor-capacitor (RC) filter. By coupling this emulator to the classical Chua’s circuit in parallel in both forward and reverse ways, two asymmetric memristive Chua’s circuits are proposed and their mathematical models are established. Because of the symmetry between the forward and reverse circuits, the forward memristive Chua’s (FAMC) circuit is focused on modelling the normalised system and investigating the equilibrium stability. With the FAMC system, several numerical plots are employed to discuss the parameter-dependent complex dynamics and initial-dependent coexisting behaviours. The numerical results manifest that there are three equilibrium points in the FAMC system, among which two non-zero equilibrium points are asymmetric, resulting in the emergence of asymmetric attractors. With the change of system parameters, the stability of one non-zero equilibrium point converts from unstable saddle-focus into stable node-focus, leading to the coexistence of multiple attractors. In addition, hardware experiments on a breadboard level are executed and the captured results well verify the numerical plots.

摘要

压缩磁滞回线的不对称特性通常出现在真正的忆阻器中。为了模仿这一特性，非对称忆阻器仿真器由一个模拟电路构成，该电路由一个非平衡二极管桥和一个电阻电容 (RC) 滤波器组成。通过将该仿真器以正向和反向方式并联耦合到经典蔡氏电路，提出了两种非对称忆阻蔡氏电路并建立了它们的数学模型。由于正向和反向电路之间的对称性，正向忆阻蔡氏 (FAMC) 电路专注于对归一化系统进行建模并研究平衡稳定性。使用 FAMC 系统，使用几个数值图来讨论依赖于参数的复杂动力学和依赖于初始的共存行为。数值结果表明，FAMC系统存在三个平衡点，其中两个非零平衡点不对称，导致出现不对称吸引子。随着系统参数的变化，一个非零平衡点的稳定性从不稳定的鞍形焦点转变为稳定的节点焦点，导致多个吸引子并存。此外，还执行了面包板级别的硬件实验，捕获的结果很好地验证了数值图。导致多个吸引子共存。此外，还执行了面包板级别的硬件实验，捕获的结果很好地验证了数值图。导致多个吸引子共存。此外，还执行了面包板级别的硬件实验，捕获的结果很好地验证了数值图。