Multiple almost periodic solutions in nonautonomous delayed neural networks

Kuang Hui Lin*, Chih-Wen Shih

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2 n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

Original languageEnglish
Pages (from-to)3392-3420
Number of pages29
JournalNeural Computation
Volume19
Issue number12
DOIs
StatePublished - 1 Dec 2007

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