scholarly journals Stability of Delayed Hopfield Neural Networks with Variable-Time Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yangjun Pei ◽  
Chao Liu ◽  
Qi Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Fixed Time ◽  
Hopfield Neural Networks ◽  
Stability Criteria ◽  
Variable Time ◽  
Numerical Example ◽  
Globally Exponential Stability ◽  
Theoretical Results

In this paper the globally exponential stability criteria of delayed Hopfield neural networks with variable-time impulses are established. The proposed criteria can also be applied in Hopfield neural networks with fixed-time impulses. A numerical example is presented to illustrate the effectiveness of our theoretical results.

Effects of variable-time impulses on global exponential stability of Cohen–Grossberg neural networks

2017 ◽  
Vol 10 (08) ◽  
pp. 1750117 ◽  
Author(s):  
Xianxiu Zhang ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Hafiz Gulfam Ahmad
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Equilibrium Points ◽  
Fixed Time ◽  
Stability Criteria ◽  
Impulsive Systems ◽  
Comparison System ◽  
Variable Time ◽  
Theoretical Results

We investigate the global exponential stability of Cohen–Grossberg neural networks (CGNNs) with variable moments of impulses using B-equivalence method. Under certain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.

scholarly journals Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

2013 ◽  
Vol 23 (1) ◽  
pp. 201-211 ◽  
Author(s):  
Yang Liu ◽  
Rongjiang Yang ◽  
Jianquan Lu ◽  
Bo Wu ◽  
Xiushan Cai
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
High Order ◽  
Impulsive Effect ◽  
Time Varying ◽  
Stability Criteria ◽  
Globally Exponential Stability ◽  
Impulsive Differential Inequality

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

EXPONENTIAL STABILITY OF A CLASS OF POSITIVE NONLINEAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

2020 ◽  
Vol 65 (6) ◽  
pp. 3-12
Author(s):  
Dung Le Thi Hong
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Exponential Stability ◽  
Hopfield Neural Networks ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Time Varying ◽  
System State ◽  
Numerical Example ◽  
Comparison Technique

This paper is concerned with the problem of exponential stability of a class of positive nonlinear systems with heterogeneous time-varying delays which describe a model of Hopfield neural networks with nonlinear self-inhibition rates. Based on a novel comparison technique via a differential and integral inequalities, testable conditions are derived to ensure system state trajectories converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.

scholarly journals pth Moment Exponential Stability of Stochastic PWM Feedback Systems with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Zhong Zhang ◽  
Lixia Ye
Keyword(s):  
Exponential Stability ◽  
Pulse Width ◽  
Time Varying ◽  
Stability Criteria ◽  
Feedback Systems ◽  
Pulse Width Modulated ◽  
Globally Exponential Stability ◽  
Pth Moment Exponential Stability ◽  
Moment Exponential Stability ◽  
Theoretical Results

This paper further studies thepth moment exponential stability of stochastic pulse-width-modulated (PWM) feedback systems with distributed time-varying delays. We establish several globally exponential stability criteria for such PWM feedback systems by using Lyapunov-Krasovskii functional and then present an upper bound of the parameter of PWM when the system is stable and such system has stronger anti-interference performance than the system without time-varying delays. Furthermore, we present two examples to show the effectiveness and conservativeness of the theoretical results.

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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