Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks

Linna Liu and Quanxin Zhu

Applied Mathematics and Computation, 2015, vol. 266, issue C, 698-712

Abstract: Stability of numerical solutions to stochastic delay differential equations have received an increasing attention, but there has been so far little work on the stability analysis of numerical solutions to stochastic delay Hopfield neural networks. The aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks by using two approaches: the Euler method and the backward Euler method. Under some reasonable conditions, both the Euler scheme and the backward Euler scheme are proved to be almost sure exponential stability. In particular, the Euler method and the backward Euler method are mainly based on the semimartingale convergence theorem.

Keywords: Stochastic delay Hopfield neural network; Euler method; Backward Euler method; Almost sure exponential stability (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:698-712

DOI: 10.1016/j.amc.2015.05.134

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