Multistability and convergence in delayed neural networks

Chang Yuan Cheng, Kuang Hui Lin, Chih-Wen Shih*

*Corresponding author for this work

Research output: Contribution to journalArticle

102 Scopus citations

Abstract

We present the existence of 2n stable stationary solutions for a general n-dimensional delayed neural networks with several classes of activation functions. The theory is obtained through formulating parameter conditions motivated by a geometrical observation. Positively invariant regions for the flows generated by the system and basins of attraction for these stationary solutions are established. The theory is also extended to the existence of 2n limit cycles for the n-dimensional delayed neural networks with time-periodic inputs. It is further confirmed that quasiconvergence is generic for the networks through justifying the strongly order preserving property as the self-feedback time lags are small for the neurons with negative self-connection weights. Our theory on existence of multiple equilibria is then incorporated into this quasiconvergence for the network. Four numerical simulations are presented to illustrate our theory.

Original languageEnglish
Pages (from-to)61-74
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Volume225
Issue number1
DOIs
StatePublished - 1 Jan 2007

Keywords

  • Convergence
  • Monotone dynamics
  • Multistability
  • Neural networks

Fingerprint Dive into the research topics of 'Multistability and convergence in delayed neural networks'. Together they form a unique fingerprint.

  • Cite this