Globally asymptotic stability analysis for memristor‐based competitive systems of reaction–diffusion delayed neural networks

Abstract

The main aim of this investigation is to present a mathematical criterion that guarantees the global asymptotic stability of special class of nonlinear neural systems. Indeed, a memristor‐based competitive nonlinear reaction–diffusion Cohen–Grossberg neural network system is chosen to be investigated. Chasing the accuracy and comprehensiveness, our model has to be improved with the following elements: neutrality of the nonlinear part and being effected under time delays in the both of straight and neutral parts of the nonlinearity. Since the proposed neural network is novel, so we need to make use of a novel Lyapunov functional correspondingly to globally asymptotic stabilization of the neural network under investigation. Prior to this process, it is necessary to present a uniqueness criterion for solutions of the proposed neural network. To this aim, the well‐known M‐matrix technique of the linear algebra is applied that guarantees existence of a unique equilibrium point of the considered Cohen–Grossberg neural network. Numerical perspective of this investigation leads us to some numerical prototypes that justify our stability criterion is applicable. This investigation will be finalized with interesting discussion on the nature of time delays that are characterized as fundamental elements in modeling of the neural networks.