Existence and global asymptotic stability of positive periodic solution of delayed Cohen-Grossberg neural networks

Abstract In this paper, a class of periodic Cohen–Grossberg neural networks with discrete and distributed time-varying delays is considered. By an extension of the Lyapunov–Krasovskii functional method, a novel criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is derived in terms of M-matrix without any restriction on uniform positiveness of the amplification functions. Comparison and illustrative examples are given to illustrate the effectiveness of the obtained results.

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