Multistability of Switched Neural Networks With Gaussian Activation Functions Under State-Dependent Switching.
Journal:
IEEE transactions on neural networks and learning systems
Published Date:
Oct 27, 2022
Abstract
This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of 753 equilibrium points, and 432 of them are locally stable, wherein p , p , and p are nonnegative integers satisfying 0 ≤ p+p+p ≤ n and n is the number of neurons. It implies that there exist up to 7 equilibria, and up to 4 of them are locally stable when p=n . It also implies that properly selecting p , p , and p can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.