Existence and exponential stability of periodic solution for impulsive delay differential equations and applications |
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Authors: | Zhichun Yang Daoyi Xu |
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Institution: | Institute of Mathematics, Sichuan University, Chengdu 610064, PR China |
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Abstract: | In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay differential equations. Furthermore, the criteria are applied to analyze dynamical behavior of impulsive delay Hopfield neural networks and the results show different behavior of impulsive system originating from one continuous system. |
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Keywords: | Exponential stability Periodic solution Impulsive delay differential equations (IDDEs) |
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