Existence, uniqueness, and stability analysis of impulsive neural networks with mixed time delays
type: Item
instance of: scholarly article
title: Existence, uniqueness, and stability analysis of impulsive neural networks with mixed time delays
zbMATH Open document ID: 1470.34221
DOI: 10.1155/2014/327070
author: Qiang Xi
author: Jianguo Si
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results.
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 7022177
Wikidata QID: Q59036203
describes a project that uses: LMI toolbox
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/327070
OpenAlex ID: W2079668247
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description: scientific article; zbMATH DE number 7022177