Stability of stochastic delay neural networks

Steve Blythe, Xuerong Mao, Xiaoxin Liao

Research output: Contribution to journalArticle

285 Citations (Scopus)

Abstract

The authors in their papers (Liao and Mao, Stochast. Anal. Appl. 14 (2) (1996a) 165-185; Neural, Parallel Sci. Comput. 4 (2) (1996b) 205-244) initiated the study of stability and instability of stochastic neural networks and this paper is the continuation of their research in this area. The main aim of this paper is to discuss almost sure exponential stability for a stochastic delay neural network dx(t) = [-Bx(t) + Ag(xτ(t))]dt + σ(x(t),g(xτ(t),t)dw(t). The techniques used in this paper are different from those in their earlier papers. Especially, the nonnegative semimartingale convergence theorem will play an important role in this paper. Several examples are also given for illustration.

LanguageEnglish
Pages481-495
Number of pages15
JournalJournal of the Franklin Institute
Volume338
Issue number4
DOIs
Publication statusPublished - Jul 2001

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Almost Sure Exponential Stability
Stochastic Neural Networks
Semimartingale
Convergence Theorem
Continuation
Non-negative
Neural Networks
Neural networks
Asymptotic stability

Keywords

  • Brownian motion
  • delay neural network
  • exponential stability
  • Lyapunov exponent
  • Martingale convergence theorem

Cite this

Blythe, Steve ; Mao, Xuerong ; Liao, Xiaoxin. / Stability of stochastic delay neural networks. In: Journal of the Franklin Institute. 2001 ; Vol. 338, No. 4. pp. 481-495.
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Stability of stochastic delay neural networks. / Blythe, Steve; Mao, Xuerong; Liao, Xiaoxin.

In: Journal of the Franklin Institute, Vol. 338, No. 4, 07.2001, p. 481-495.

Research output: Contribution to journalArticle

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