Global asymptotic stability of impulsive CNNs with proportional delays and partially Lipschitz activation functions
type: Item
instance of: scholarly article
title: Global asymptotic stability of impulsive CNNs with proportional delays and partially Lipschitz activation functions
zbMATH Open document ID: 1474.34510
DOI: 10.1155/2014/832892
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation \(v_i(t) = u_i(e^t)\), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 7023160
Wikidata QID: Q59041879
author: Xueli Song
author: Ji-Gen Peng
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/832892
OpenAlex ID: W2056272344
cites work: Cellular neural networks: theory
cites work: On stability of cellular neural networks with delay
cites work: Equilibrium Analysis of Cellular Neural Networks
cites work: The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$
cites work: On neutral functional-differential equations with proportional delays
cites work: Global exponential stability of impulsive cellular neural networks with time-varying delays via fixed point theory
cites work: New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays
cites work: On global exponential stability for impulsive cellular neural networks with time-varying delays
cites work: Exponential stability of delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions
cites work: Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays
cites work: Global exponential stability for impulsive cellular neural networks with time-varying delays
cites work: Global exponential stability analysis on impulsive BAM neural networks with distributed delays
cites work: Exponential stability of artificial neural networks with distributed delays and large impulses
cites work: Global exponential stability of impulsive Cohen-Grossberg neural networks with continuously distributed delays
cites work: Global exponential stability of cellular neural networks with continuously distributed delays and impulses
cites work: Global exponential stability of BAM neural networks with distributed delays and impulses
cites work: Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse
cites work: Multistability in impulsive hybrid Hopfield neural networks with distributed delays
cites work: New conditions for global stability of neural networks with application to linear and quadratic programming problems
cites work: Q4003237
cites work: New convergence behavior of solutions to shunting inhibitory cellular neural networks with unbounded delays and time-varying coefficients
cites work: Complete stability of cellular neural networks with unbounded time-varying delays
cites work: A unified synchronization criterion for impulsive dynamical networks
cites work: Single impulsive controller for globally exponential synchronization of dynamical networks
cites work: Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay
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description: scientific article; zbMATH DE number 7023160