Abstract
In this paper, we first propose a concept of compact almost automorphic functions on time scales, and study some basic properties of compact almost automorphic functions on time scales, including an equivalent characterization of compact almost automorphic functions on time scales, composition theorems of compact almost automorphic functions and the completeness of the space of compact almost automorphic functions. Then, as an application of our results, we prove the existence and global exponential stability of a class of Clifford-valued recurrent neural networks with time-varying delays on time scales, and demonstrate the feasibility of our results by an example.
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The authors would like to thank the Editor and the anonymous referees for their helpful comments and valuable suggestions regarding this article.
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This work is supported by the National Natural Science Foundation of China under Grant 11861072.
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Li, Y., Shen, S. Compact Almost Automorphic Function on Time Scales and Its Application. Qual. Theory Dyn. Syst. 20, 86 (2021). https://doi.org/10.1007/s12346-021-00522-5
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DOI: https://doi.org/10.1007/s12346-021-00522-5
Keywords
- Compact almost automorphic functions
- Dynamic equations on time scales
- Clifford-valued recurrent neural networks
- Global exponential stability