Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps

2020 ◽  
Vol 545 ◽  
pp. 123782
Author(s):  
Jianguo Tan ◽  
Yahua Tan ◽  
Yongfeng Guo ◽  
Jianfeng Feng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Numerical Solutions ◽  
Hopfield Neural Networks ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability

scholarly journals Almost sure exponential stability of delayed Hopfield neural networks

2008 ◽  
Vol 21 (7) ◽  
pp. 701-705 ◽  
Author(s):  
Chuangxia Huang ◽  
Ping Chen ◽  
Yigang He ◽  
Lihong Huang ◽  
Wen Tan
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
Almost Sure Exponential 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.

scholarly journals Inequalities and pth moment exponential stability of impulsive delayed Hopfield neural networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yutian Zhang ◽  
Guici Chen ◽  
Qi Luo
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
New Method ◽  
Integral Inequalities ◽  
Delay Function ◽  
Pth Moment Exponential Stability ◽  
Moment Exponential Stability

AbstractIn this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities. Our discussion neither requires a complicated Lyapunov function nor the differentiability of the delay function. In addition, we also summarize a new result on the exponential stability of a class of impulsive integral inequalities. Finally, one example is given to illustrate the effectiveness of the obtained results.

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