具有平衡线系统的亚临界Andronov-Hopf方案
Subcritical Andronov-Hopf scenario for systems with a line of equilibria
摘要：
利用数值模拟方法和分析方法，我们证明了硬自激振荡激发系统的无穷多个平衡点形成一条线的相空间中的平衡。所研究的分岔现象是等效的激励方案通过亚临界Andronov-Hopf分岔观察到的经典自振子孤立的平衡点。所讨论的过程中伴随的滞后和双稳态显示和解释。以一个基于忆阻器的非线性自振子模型为例进行了研究。首先，一个更简单的模型，包括蔡氏忆阻器与分段平滑特性进行了探讨。然后，忆阻器特性被改变为处处平滑的函数。最后，考虑了忆阻器遗忘效应的作用。
英文摘要：
Using numerical simulation methods and analytical approach, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
