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Convergence and stability of the split-step \(\theta\)-Milstein method for stochastic delay Hopfield neural networks. (English) Zbl 1271.92003

Summary: 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 \(\theta\)-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 \(\theta\)-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.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92-08 Computational methods for problems pertaining to biology
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