Passivity And Synchronization Of Coupled-reaction-spreading Neural Networks With Pulse Effects

In recent years,the impulsive control technique has been widely applied to realize synchronization for complex networks due to reduced control cost.Obviously,it is very significant to utilize the impulsive control method to investigate synchronization issue for coupled reaction-diffusion neural networks.Unfortunately,there are very few results concerning this problem.On the other hand,the passive properties of systems can keep the systems internally stable.So the passivity theory has found fruitfful applications in various fields such as signal processing,stability,complexity,chaos control and synchronization,fuzzy control and so on.To the best of our knowledge,the passivity of impulsive coupled reaction-diffusion neural networks has not yet been considered.Therefore,we respectively investigate the passivity of coupled reaction-diffusion neural networks with impulsive effects and impulsive control for the synchronization of coupled neural networks with reaction-diffusion terms.The main contents of this paper are as follows:1.Passivity analysis of coupled reaction-diffusion neural networks with impulsive effectsBy constructing appropriate Lyapunov functionals and utilizing the matrix theory,the graph theory and the inequality techniques,we respectively establish several criteria for the input strict passivity and output strict passivity of impulsive coupled reaction-diffusion neural networks with and without time-varying delay.Finally,two numerical examples are given to verify the correctness of the proposed results.2.Impulsive control for the synchronization of coupled reaction-diffusion neural networksBy combining the Lyapunov functional method with the impulsive delay differential inequality and comparison principle,some criteria are established to guarantee the global exponential synchronization of coupled reaction-diffusion neural networks.In addition,the estimate for the exponential convergence rate is also given,which relies on time delay,system parameters and impulsive interval.Finally,we provide numerical examples to illustrate the validity and effectiveness of the main results.