Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays

In this Letter, we study a class of reaction-diffusion cellular neural networks with delays by introducing ingeniously real parameters xi(*)(j), eta(*)(j), alpha(*)(j), beta(*)(j), eta(j), beta(j) with xi(*)(j) + alpha(*)(j) = 1, eta(*)(j) + beta(*)(j) = 1, xi(j) + alpha(j) = 1, eta(j) + beta(j) = 1 (j = 1,...,n), employing suitable Lyapunov functionals and applying some inequality techniques, we obtain a set of sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic oscillatory solution. These conditions have important leading significance in the design and applications of periodic oscillatory reaction-diffusion neural circuits. (c) 2005 Elsevier B.V. All rights reserved.