Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays

Peng Liu, Zhigang Zeng, Jun Wang

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

This paper addresses the multistability for a general class of recurrent neural networks with time-varying delays. Without assuming the linearity or monotonicity of the activation functions, several new sufficient conditions are obtained to ensure the existence of (2K+1)n equilibrium points and the exponential stability of (K+1)n equilibrium points among them for n-neuron neural networks, where K is a positive integer and determined by the type of activation functions and the parameters of neural network jointly. The obtained results generalize and improve the earlier publications. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of these exponentially stable equilibrium points can be larger than their originally partitioned subsets. Finally, three illustrative numerical examples show the effectiveness of theoretical results.

Original languageEnglish
Pages (from-to)117-127
Number of pages11
JournalNeural Networks
Volume79
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

Keywords

  • Cohen-Grossberg neural networks
  • Multistability
  • Non-monotonic activation functions
  • Time-varying delays

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