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Existence and attractivity of periodic solutions to non-autonomous Cohen-Grossberg neural networks with time delays. (English) Zbl 1198.34139

Summary: We investigate the existence and attractivity of periodic solutions to non-autonomous Cohen-Grossberg neural networks with connection time delays for both discrete and distributed cases. By combining the Lyapunov functional method with the contraction mapping principle, we establish several criteria for the existence and global exponential stability of periodic solutions. More interestingly, all the criteria are independent of time delays as well as the delay types, and do not include one another. Several examples with numerical simulations are given to demonstrate the results.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34K13Periodic solutions of functional differential equations
34D23Global stability of ODE
92B20General theory of neural networks (mathematical biology)