Impulsive Systems on Hybrid Time Domains

Abstract

the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

“…The following comparison lemma can be proved by the same arguments used for the comparison results in [15,28,29]. ϕ(0, .…”

“…Definition 2 is a generalization of the stability of sets definitions [48,49,53] to the reaction-diffusion case. What follows are definitions and a comparison lemma from the Lyapunov-Razumikhin method [15,19,28,29,42,46].…”

“…On the other hand, considering impulsive perturbations in CGNNs is a very hot topic of interest [20][21][22][23][24]. It has been found that, because of some instantaneous perturbations, the behaviors of many real-word systems are not continuous processes, and such processes can be modelled by impulsive differential equations [25][26][27][28][29]. Therefore, it is crucial to study the dynamic properties of impulsive reaction-diffusion CGNNs, and numerous excellent qualitative results have been published.…”

Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

“…In order to study the robust stability behavior of a Cohen-Grossberg neural network with uncertain parameters and distributed delays with respect to h−manifolds, an effective approach is proposed in this research using discrete control via variable impulsive perturbations. To this end, we will apply the theory of impulsive differential equations, which are useful tools in the design of impulsive control strategies [30], [36]- [38]. Impulsive controllers and impulsive control methods have been intensively applied to different mathematical models [39]- [45] including neural network systems [46]- [50].…”

On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

“…Since impulsive phenomena exist in numerous fields of science and engineering [25][26][27][28][29] and the impulsive control methods are find to be more efficient than other control strategies [30][31][32][33][34][35][36][37][38], there has been an increasing research interest on the impulsive generalizations of Cohen-Grossberg-type BAM neural networks with delays. For example, in [39] the problem of existence of equilibrium states of Cohen-Grossberg BAM neural networks with delays and impulses and their global exponential stability behavior are investigated using topological degree theory, the Lyapunov functional method and some analysis techniques.…”