Bursting Oscillations and the Formation Mechanism in a Piecewise Linear Memristive System
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摘要: 为了研究分段线性忆阻系统的簇发振荡及其形成机理，该文在一非自治系统中引入分段线性忆阻器模型与慢变化的周期激励项，建立了一种两时间尺度的4D分段线性忆阻系统。由于分段线性忆阻器模型的引入，系统被非光滑分界面分成不同的子系统。相应子系统控制的名义平衡轨迹的稳定性与非光滑分界面均会影响系统的簇发现象，导致轨迹在非光滑分界面处的突然跃迁与非光滑分岔的产生，从而展现出两种不同机理的簇发模式。利用微分包含定理对分岔机理进行分析，并借助时序图、转换相图等，通过数值仿真与Multisim电路仿真验证了理论分析的正确性，该文对分段线性忆阻系统的动力学行为及应用研究具有重要意义。Abstract: In order to explore the bursting oscillations and its mechanism of the piecewise linear memristor-based system, a 4D piecewise linear memristor-based system with two-timescale is created by introducing a piecewise linear memristive model and a periodically excitation based on a non-autonomous system. Due to the introduction of the piecewise linear memristive model, the system is divided into different subsystems by non-smooth boundaries. It is pointed that not only the stability of the nominal equilibrium orbits but also the non-smooth boundaries may influence the bursting, resulting in the abrupt jumping of the trajectory and non-smooth bifurcations, which reveal two different bursting patterns. Based on the generalized differential of Clarke, the bifurcation mechanism is studied. And the bursting mechanism is analyzed by time history and transformation phase diagram. Finally, the numerical simulation and Multisim circuit simulation are conducted to verify the validity. This paper is of great significance to study the dynamical behavior of the piecewise linear memristor and its application to practice.
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