Mean square stability of two classes of theta methods for numerical computation and simulation of delayed stochastic Hopfield neural networks

2018 ◽  
Vol 343 ◽  
pp. 428-447 ◽  
Author(s):  
Linna Liu ◽  
Feiqi Deng ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Numerical Computation ◽  
Hopfield Neural Networks ◽  
Mean Square ◽  
Mean Square Stability

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

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Qian Guo ◽  
Wenwen Xie ◽  
Taketomo Mitsui
Keyword(s):  
Neural Networks ◽  
Linear Growth ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Growth Conditions ◽  
Hopfield Neural Networks ◽  
Mean Square ◽  
Stochastic Delay ◽  
Mean Square Stability ◽  
Milstein Method

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-stepθ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher than that of existing split-stepθ-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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