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On periodic solutions to a class of non-autonomously delayed reaction-diffusion neural networks. (English) Zbl 1221.35200
Summary: 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.
MSC:
35K57Reaction-diffusion equations
35B10Periodic solutions of PDE
92B20General theory of neural networks (mathematical biology)
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