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Almost periodic solutions to dynamic equations on time scales and applications. (English) Zbl 1251.34060

Summary: We first introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.

MSC:

34C25 Periodic solutions to ordinary differential equations
34N05 Dynamic equations on time scales or measure chains
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