A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled by the system parameters. The complex dynamics of the system are analyzed by using compound coexisting bifurcation diagrams, Lyapunov exponent spectra and phase portraits, including point attractors, limit cycles, symmetrical chaotic attractors and their blasting, extreme multistability, state-switching without parameter, and transient chaos. Of particular surprise is that the extreme multistability of the system is hidden and symmetrically distributed. It is found that the existence of transient chaos in the specified parameter domain is determined by using bifurcation diagrams within different time durations and Lyapunov exponents with chaotic sequences. Finally, the symmetrical chaotic attractor and the system blasting are verified by digital signal processing experiments, which are consistent with the numerical analysis.

中文翻译：

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基于忆阻器的混沌系统的极端多稳定性和复杂动力学

提出并分析了一种具有共存收缩磁滞回线和双局部活动域的忆阻器，并设计了一个仿真器并将其应用于经典的 Chua 电路以代替二极管。忆阻系统采用四个耦合的一阶自主微分方程建模，其中三个平衡由忆阻器的三个静态平衡决定，但不受系统参数控制。利用复合共存分岔图、李雅普诺夫指数谱和相图分析了系统的复杂动力学，包括点吸引子、极限环、对称混沌吸引子及其爆破、极端多稳态、无参数状态切换和瞬态混沌。特别令人惊讶的是，系统的极端多稳定性是隐藏的并且是对称分布的。发现在指定参数域中是否存在瞬态混沌是通过使用不同时长内的分岔图和具有混沌序列的Lyapunov指数来确定的。最后，通过数字信号处理实验验证了对称混沌吸引子和系统爆破，与数值分析一致。