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

Date
2019-12-21
Authors
Stamov, Gani
Tomasiello, Stefania
Stamova, Ivanka
Spirova, Cvetelina
Journal Title
Journal ISSN
Volume Title
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Abstract

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

Description
Keywords
stability of sets, Cohen-Grossberg neural networks, impulsive perturbations, delays
Citation
Mathematics 8 (1): 27 (2020)
Department
Mathematics