This paper presents a bi-directional N-type locally-active memristor (LAM) model, which has two symmetrical locally-active regions with respect to the origin. For this memristor, the locally-active regions coincide with the edge of chaos regimes, where complex dynamic behaviors may occur. By deriving the small-signal admittance of the memristor, it is found that the LAM may be pure resistive, inductive or capacitive in terms of biasing voltages. When the LAM operates at the edge of chaos and connects with an external inductor in series, a second-order periodic oscillator is established. In this case, it is possible to move the poles of the system from the left-half plane to the right-half plane, thereby generating periodic oscillations. Complex dynamics of the second-order memristor-based oscillator is analyzed via Hopf bifurcation analysis and based on the theories of local activity and edge of chaos. Using the parasitic capacitor of the LAM in the second-order oscillator, a third-order chaotic oscillator is designed, which has a negative real pole and a pair of complex conjugate poles with positive real parts, satisfying the Shilnikov criterion. It is found that both periodic oscillation and chaos appear only at the edge of chaos of the LAM, thus verifying the complexity theorem, no-complexity theorem and edge of chaos theorem. Finally, circuit experiments are performed, which verify the dynamics and the effectiveness of the LAM model, the periodic oscillator and the chaotic oscillator.

本文提出了一种双向 N 型局部有源忆阻器 (LAM) 模型，该模型具有两个相对于原点对称的局部有源区域。对于这种忆阻器，局部活性区域与混沌状态的边缘重合，在那里可能会发生复杂的动态行为。通过推导忆阻器的小信号导纳，发现 LAM 在偏置电压方面可能是纯电阻性、电感性或电容性的。当 LAM 工作在混沌边缘并与外部电感串联时，建立一个二阶周期振荡器。在这种情况下，可以将系统的极点从左半平面移动到右半平面，从而产生周期性振荡。通过Hopf分岔分析并基于局部活动和混沌边缘理论，分析了基于二阶忆阻器的振荡器的复杂动力学。利用二阶振荡器中LAM的寄生电容，设计了一个三阶混沌振荡器，它具有一个负实极和一对具有正实部的复共轭极，满足Shilnikov准则。发现周期振荡和混沌都只出现在LAM的混沌边缘，从而验证了复杂性定理、非复杂性定理和混沌边缘定理。最后，进行了电路实验，验证了LAM模型、周期振荡器和混沌振荡器的动力学和有效性。利用二阶振荡器中LAM的寄生电容，设计了一个三阶混沌振荡器，它具有一个负实极和一对具有正实部的复共轭极，满足Shilnikov准则。发现周期振荡和混沌都只出现在LAM的混沌边缘，从而验证了复杂性定理、非复杂性定理和混沌边缘定理。最后，进行了电路实验，验证了LAM模型、周期振荡器和混沌振荡器的动力学和有效性。利用二阶振荡器中LAM的寄生电容，设计了一个三阶混沌振荡器，它具有一个负实极和一对具有正实部的复共轭极，满足Shilnikov准则。发现周期振荡和混沌都只出现在LAM的混沌边缘，从而验证了复杂性定理、非复杂性定理和混沌边缘定理。最后，进行了电路实验，验证了LAM模型、周期振荡器和混沌振荡器的动力学和有效性。发现周期振荡和混沌都只出现在LAM的混沌边缘，从而验证了复杂性定理、非复杂性定理和混沌边缘定理。最后，进行了电路实验，验证了LAM模型、周期振荡器和混沌振荡器的动力学和有效性。发现周期振荡和混沌都只出现在LAM的混沌边缘，从而验证了复杂性定理、非复杂性定理和混沌边缘定理。最后，进行了电路实验，验证了LAM模型、周期振荡器和混沌振荡器的动力学和有效性。