具有平衡线的忆阻振荡器无参数稳态分岔的广义模型
Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria
摘要：
我们演示了如何干草叉，跨临界和鞍结分岔的动力系统中观察到的稳定状态与有限数量的孤立的平衡点发生在系统的平衡线。探索是通过使用数值模拟和线性稳定性分析应用到一个模型的忆阻器为基础的振荡器。首先，所有讨论的分歧的情况下，被认为是在系统的上下文中，包括蔡氏忆阻器与分段光滑特性。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。所给出的结果是电子电路模型，但所考虑的分叉现象可以表现出任何性质的平衡线的系统。
英文摘要：
We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based oscillator. First, all the discussed bifurcation scenarios are considered in the context of systems including Chua's memristor with a piecewise-smooth characteristic. Then the memristor characteristic is changed to a function that is smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration. The presented results are obtained for electronic circuit models, but the considered bifurcation phenomena can be exhibited by systems with a line of equilibria of any nature.
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