论文标题
在基于备忘录的振荡器中，具有平衡线的稳态分叉的通用模型
Generalized model for steady-state bifurcations without parameters in memristor-based oscillators with lines of equilibria
论文作者
论文摘要
我们展示了在具有有限数量的孤立平衡点的动力系统中观察到的稳态的干草叉，跨批评和鞍节点分叉如何发生在具有平衡线的系统中。探索是通过使用应用于基于Memristor的振荡器模型的数值模拟和线性稳定性分析来进行的。首先，在包括Chua的Memristor（具有分段平滑的特征）的系统中，考虑了所有讨论的分叉场景。然后，Memristor特性将其更改为到处平稳的函数。最后，考虑了备忘录遗忘效果的作用。对电子电路模型获得了呈现的结果，但是所考虑的分叉现象可以通过具有任何性质平衡的系统表现出来。
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.
