Convergence and Stability of the Split-Stepθ-Milstein Method for Stochastic Delay Hopfield Neural Networks | Zendy

Qian Guo | Zendy; Wenwen Xie | Zendy; Taketomo Mitsui | Zendy

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

Author(s) -

Qian Guo,

Wenwen Xie,

Taketomo Mitsui

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/169214

Subject(s) - mathematics , convergence (economics) , stability (learning theory) , algorithm , lipschitz continuity , artificial neural network , machine learning , computer science , mathematical analysis , economics , economic growth

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

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