Multistability of switched neural networks with sigmoidal activation functions under state-dependent switching

This paper presents theoretical results on the multistability of switched neural networks with commonly used sigmoidal activation functions under state-dependent switching. The multistability analysis with such an activation function is difficult because state-space partition is not as straightforward as that with piecewise-linear activations. Sufficient conditions are derived for ascertaining the existence and stability of multiple equilibria. It is shown that the number of stable equilibria of an n-neuron switched neural networks is up to 3(n) under given conditions. In contrast to existing multistability results with piecewise-linear activation functions, the results herein are also applicable to the equilibria at switching points. Four examples are discussed to substantiate the theoretical results. (c) 2019 Elsevier Ltd. All rights reserved.