Exponential stability of numerical solutions to stochastic delay Hopfield neural networks

2010 ◽  
Vol 73 (4-6) ◽  
pp. 920-926 ◽  
Author(s):  
Li Ronghua ◽  
Pang Wan-kai ◽  
Leung Ping-kei
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Numerical Solutions ◽  
Hopfield Neural Networks ◽  
Stochastic Delay

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.

Split-Step Backward Euler Method for Stochastic Delay Hopfield Neural Networks with Markovian Switching

2011 ◽  
Vol 58-60 ◽  
pp. 1390-1395
Author(s):  
Rong Hua Li ◽  
Li Yang ◽  
Jia Wei Li
Keyword(s):  
Neural Networks ◽  
Euler Method ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Backward Euler Method ◽  
Approximation Solution ◽  
True Solution ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Exponentially Stable

In this paper, split-step backward Euler method for stochastic delay Hopfield neural networks with Markovian switching is considered. The main aim of this paper is to show that the numerical approximation solution is convergent to the true solution with order. The conditions under which the numerical solution is exponentially stable in mean square are given. An example is provided for illustration.

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