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

Gani Stamov, Ivanka Stamova, George Venkov, Trayan Stamov and Cvetelina Spirova
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Gani Stamov: Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
George Venkov: Department of Mathematical Analysis and Differential Equations, Technical University of Sofia, 1000 Sofia, Bulgaria
Trayan Stamov: Department of Machine Elements and Non-metallic Constructions, Technical University of Sofia, 1000 Sofia, Bulgaria
Cvetelina Spirova: Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria

Mathematics, 2020, vol. 8, issue 7, 1-18

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 Poincar?-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.

Keywords: integral manifolds; Cohen–Grossberg-type neural networks; delays; reaction–diffusion terms; variable impulsive perturbations; boundedness; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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