IEEE Trans Cybern. 2022 Jun;52(6):4701-4716. doi: 10.1109/TCYB.2020.3034249. Epub 2022 Jun 16.
This article is concerned with the problem of the number and dynamical properties of equilibria for a class of connected recurrent networks with two switching subnetworks. In this network model, parameters serve as switches that allow two subnetworks to be turned ON or OFF among different dynamic states. The two subnetworks are described by a nonlinear coupled equation with a complicated relation among network parameters. Thus, the number and dynamical properties of equilibria have been very hard to investigate. By using Sturm's theorem, together with the geometrical properties of the network equation, we give a complete analysis of equilibria, including the existence, number, and dynamical properties. Necessary and sufficient conditions for the existence and exact number of equilibria are established. Moreover, the dynamical property of each equilibrium point is discussed without prior assumption of their locations. Finally, simulation examples are given to illustrate the theoretical results in this article.
这篇文章关注的是一类具有两个切换子网的连通递归网络的平衡点的数量和动态特性的问题。在这个网络模型中，参数充当开关，可以在不同的动态状态之间打开或关闭两个子网。这两个子网由一个具有网络参数之间复杂关系的非线性耦合方程来描述。因此，平衡点的数量和动态特性很难研究。通过使用 Sturm 定理以及网络方程的几何性质，我们对平衡点进行了全面的分析，包括平衡点的存在性、数量和动态特性。建立了平衡点存在和确切数量的充分必要条件。此外，无需先验假设平衡点的位置，就可以讨论每个平衡点的动态特性。最后，给出了仿真示例来说明本文的理论结果。
