Global exponential synchronization in delayed reaction-diffusion cellular neural networks with the Dirichlet boundary conditions

The global exponential synchronization for a class of delayed reaction-diffusion cellular neural networks with Dirichlet boundary conditions is discussed. Some new sufficient conditions which include the diffusion coefficients are obtained by using the Lyapunov functional method, many real parameters and inequality techniques. Particularly, different from previous works, see references [S. Li, H. Yang, X. Lou, Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms, Chaos, Solitons Fractals 40 (2009) 930–939; X. Lou, B. Cui, Asymptotic synchronization of a class of neural networks with reaction-diffusion terms and time-varying delayes, Comput. Math. Appl. 52 (2006) 897–904; Y. Wang, J. Cao, Synchronization of a class of delayed neural networks with reaction–diffusion terms, Phys. Lett. A 369 (2007) 201–211], in our results the effect of the diffusion terms on the synchronization are considered for the first time. Finally, a numerical example is given to verify our results.