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

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  • Qian Guo
  • Wenwen Xie
  • Taketomo Mitsui

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.

Suggested Citation

  • Qian Guo & Wenwen Xie & Taketomo Mitsui, 2013. "Convergence and Stability of the Split-Step -Milstein Method for Stochastic Delay Hopfield Neural Networks," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    • Handle: RePEc:hin:jnlaaa:169214
    DOI: 10.1155/2013/169214
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    Cited by:

    1. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    2. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).

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