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

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.

Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach

“…For more results on the corresponding fundamental and qualitative dynamical behaviors of impulsive reaction-diffusion systems, we refer to [ 36 , 54 , 55 , 56 , 57 ]. The consideration of impulsive conditions allows us to take into account short-term effects on susceptible cells, infected cells, and free viruses.…”

“…Next, we will define the class of Lyapunov-like functions [ 31 , 36 , 55 , 56 ] that will be used in the study of the qualitative properties of integral manifolds, related to the model (2).…”

“…For more results on the Lyapunov–Razumikhin approach applied to different models represented as classes of differential equations, we refer the reader to [ 29 , 30 , 31 , 36 , 55 , 56 , 61 ].…”

Computational Mathematics and Neural Systems

“…In [4], an extension of stability analysis methods for a class of impulsive reactiondiffusion Cohen-Grossberg delayed neural networks was formally discussed. The extended concept was related to the stability of sets.…”