Abstract
This paper is concerned with the existence and global exponential stability of periodic solutions for a nonlinear periodic system, arising from the description of the states of neurons in delayed Cohen–Grossberg type. By the continuation theorem of coincidence degree theory and Lyapunov functionals technique, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution. Some existing results are improved and extended. Even corresponding to an autonomous system, our results that these conditions are milder and less restrictive than previous known criteria since the hypothesis of boundedness and differentiability on the activation function are dropped. The theoretical analyses are verified by numerical simulations.
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