On periodic solutions to a class of non-autonomously delayed reaction-diffusion neural networks

• Published in: Communications in nonlinear science & numerical simulation Vol. 16; no. 1; pp. 414 - 422
• Main Authors: Pan, Jie, Zhan, Yongxin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2011
• Subjects: Boundary conditions; Cohen–Grossberg neural networks; Computer simulation; Criteria; Delay; Dirichlet problem; Inequalities; Lyapunov functional; Mathematical models; Neural networks; Periodic solutions; Poincaré inequality; Reaction-diffusion; Time delay; Lyapunov functional; Periodic solutions; Delay; Reaction-diffusion; Cohen–Grossberg neural networks; Poincaré inequality
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2010.02.022

In this paper, we investigate the existence and attractivity of periodic solutions for non-autonomous reaction-diffusion Cohen–Grossberg neural networks with discrete time delays. By combining the Lyapunov functional method with the contraction mapping principle and Poincaré inequality, we establish several criteria for the existence and global exponential stability of periodic solutions. More interestingly, Poincaré inequality is used to handle the reaction-diffusion terms, hence all the criteria depend on reaction-diffusion terms. These criteria are applicable in Cohen–Grossberg neural networks with both the Dirichlet and the Neumann boundary conditions on a general space domain. Several examples with numerical simulations are given to demonstrate the results.