Abstract and Applied Analysis
Volume 2013 (2013), Article ID 169214, 12 pages
http://dx.doi.org/10.1155/2013/169214
Research Article

Convergence and Stability of the Split-Step -Milstein Method for Stochastic Delay Hopfield Neural Networks

Qian Guo,1,2 Wenwen Xie,1 and Taketomo Mitsui3

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Division of Computational Science, E-Institute of Shanghai Universities, 100 Guilin Road, Shanghai 200234, China
3Department of Mathematical Sciences, Faculty of Science and Engineering, Doshisha University, Kyoto 610-0394, Japan

Received 8 December 2012; Accepted 26 February 2013

Academic Editor: Chengming Huang

Copyright © 2013 Qian Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split-step θ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher than that of existing split-step θ-method. Further, mean-square stability of the proposed method is investigated. Numerical experiments and comparisons with existing methods illustrate the computational efficiency of our method.