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

Zhenyuan Guo, Shiqin Ou, Jun Wang

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

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 3n 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.

Original languageEnglish
Pages (from-to)239-252
Number of pages14
JournalNeural Networks
Volume122
DOIs
Publication statusPublished - Feb 2020
Externally publishedYes

Keywords

  • Multistability
  • Sigmoidal activation function
  • State-dependent
  • Switched neural network

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