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Existence and exponential stability of periodic solution for impulsive delay differential equations and applications. (English) Zbl 1092.34034

A system of periodic functional-differential equations with impulses is considered. By using some differential inequalities, several results ensuring the existence of a unique globally exponentially stable periodic solution are proven.

An interesting application to a system of delayed neural networks is given. The authors claim that their results improve or extend some previous work in the same direction, even for the nonimpulsive case.

MSC:
34K13Periodic solutions of functional differential equations
34K45Functional-differential equations with impulses
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)