Multistability of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays

Peng Liu, Zhigang Zeng, Jun Wang

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

Abstract

This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an n-neuron neural network can exhibit ∧i=1n(2Ki+1) equilibrium points with Ki≥ 0. In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of ∧i=1n(Ki+1) equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.

Original languageEnglish
Pages (from-to)3000-3010
Number of pages11
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume29
Issue number7
DOIs
Publication statusPublished - Jul 2018
Externally publishedYes

Keywords

  • Multistability
  • nonmonotonic activation functions
  • recurrent neural networks
  • unbounded time-varying delays

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