Stability of stochastic delay neural networks

Steve Blythe; Xuerong Mao; Xiaoxin Liao

doi:10.1016/S0016-0032(01)00016-3

Stability of stochastic delay neural networks

Steve Blythe, Xuerong Mao^*, Xiaoxin Liao

^*Corresponding author for this work

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

344 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(x_τ(t))]dt + σ(x(t),g(x_τ(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.

Original language	English
Pages (from-to)	481-495
Number of pages	15
Journal	Journal of the Franklin Institute
Volume	338
Issue number	4
DOIs	https://doi.org/10.1016/S0016-0032(01)00016-3
Publication status	Published - Jul 2001

Keywords

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

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10.1016/S0016-0032(01)00016-3

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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.",

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T1 - Stability of stochastic delay neural networks

AU - Blythe, Steve

AU - Mao, Xuerong

AU - Liao, Xiaoxin

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AB - 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.

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KW - delay neural network

KW - exponential stability

KW - Lyapunov exponent

KW - Martingale convergence theorem

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JO - Journal of the Franklin Institute

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Stability of stochastic delay neural networks

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Keywords

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