Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations

Date
2020-07-03
Authors
Stamov, Gani
Stamova, Ivanka
Venkov, George
Stamov, Trayan
Spirova, Cvetelina
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract

The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincare`-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.

Description
Keywords
integral manifolds, Cohen–Grossberg-type neural networks, delays, reaction–diffusion terms, variable impulsive perturbations, boundedness, stability
Citation
Mathematics 8 (7): 1082 (2020)
Department
Mathematics