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\(S^{p}\)-Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays

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Abstract

In this paper, we consider Clifford-valued fuzzy cellular neural networks with time-varying delays. In order to avoid the inconvenience caused by the non-commutativity of the multiplication of Clifford numbers, we first decompose the considered n-dimensional Clifford-valued systems into \(2^{m}n\)-dimensional real-valued systems. Then by using the Banach fixed point theorem and a proof by contradiction, we establish sufficient conditions ensuring the existence, the uniqueness and the global exponential stability of \(S^{p}\)-almost periodic solutions for the considered neural networks. Finally, we give an example to illustrate the effectiveness of the obtained results. Our results are new even when the considered neural networks degenerates to real-valued, complex-valued and quaternion-valued neural networks.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11861072.

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  1. Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People’s Republic of China

    Shiping Shen & Yongkun Li

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  1. Shiping Shen
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Correspondence to Yongkun Li.

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Shen, S., Li, Y. \(S^{p}\)-Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays . Neural Process Lett 51, 1749–1769 (2020). https://doi.org/10.1007/s11063-019-10176-9

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