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

Gani Stamov, Stefania Tomasiello, Ivanka Stamova and Cvetelina Spirova
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Gani Stamov: Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria
Stefania Tomasiello: Institute of Computer Science, University of Tartu, Narva mnt 18, 51008 Tartu, Estonia
Ivanka Stamova: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
Cvetelina Spirova: Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria

Mathematics, 2019, vol. 8, issue 1, 1-20

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.

Keywords: stability of sets; Cohen-Grossberg neural networks; impulsive perturbations; delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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