Exponential synchronization of inertial reaction-diffusion coupled neural networks with proportional delay via periodically intermittent control

Abstract

This paper focuses on the global exponential synchronization problem for a class of inertial reaction-diffusion coupled neural networks with proportional delay. Through a variable transformation, the inertial reaction-diffusion neural networks are transformed into neural networks with first-order time and space derivative of the states. By taking new Lyapunov-Krasovskii functional, utilizing Wirtinger inequality, a sufficient criterion is obtained to make the addressed networks globally exponentially synchronized onto an isolated node via periodically intermittent feedback controllers. The width index, convergence rate and control gain are given through rigorous mathematical proof. Wirtinger inequality is employed to deal with the reaction-diffusion terms in a symmetric matrix form. The obtained results are easy to be verified by linear matrix inequality toolbox. The results here are also applicable to feedback control for general reaction-diffusion neural networks and inertial neural networks without any other conditions. Finally, the effectiveness and merits of the devised controllers are validated by two simulation experiments.