Multiple and Complete Stability of Recurrent Neural Networks with Sinusoidal Activation Function

Peng Liu, Jun Wang, Zhenyuan Guo

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.

Original languageEnglish
Article number9042887
Pages (from-to)229-240
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume32
Issue number1
DOIs
Publication statusPublished - Jan 2021
Externally publishedYes

Keywords

  • Countably infinite number of equilibria
  • recurrent neural networks
  • sinusoidal activation function
  • stability

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