期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 343, 期 -, 页码 428-447出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2018.04.018
关键词
Hopfield neural network; Stochastic differential equation; Time delay; Split-step theta method; Stochastic linear theta method; Mean square stability
资金
- National Natural Science Foundation of China [61503142, 61573156, 61733008]
Recently the investigation on the stability of the numerical solutions to delayed stochastic differential equations has received an increasing attention, but there has been little work on the stability analysis of the numerical solutions to delayed stochastic Hopfield neural networks (DSHNNs) so far. The aim in this paper is to study the mean square exponential stability of the split-step theta (SST) method and the stochastic linear theta (SLT) method for the underlying model. It is proved that, for any theta is an element of [0, 1/2), there exists a constant Delta* > 0 depending on theta such that the numerical schemes produced by the SST method and the SLT method are mean square exponentially stable for Delta is an element of(0, Delta*), under the same assumptions as those to guarantee the mean square exponential stability of the underlying continuous model. For the case theta is an element of [1/2, 1], we show the same stability conclusion for all Delta > 0. To carry out the required conclusion, a novel technique for the stability analysis of discrete numerical schemes with multi time delays, namely the weighted sum Lyapunov functional method, is proposed. Finally, a numerical example is given to illustrate the application of the suggested methods and to verify the stability conclusions obtained. (C) 2018 Elsevier B.V. All rights reserved.
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