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Global Mittag-Leffler Boundedness for Fractional-Order Complex-Valued Cohen–Grossberg Neural Networks

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Abstract

In this paper, a class of fractional-order complex-valued Cohen–Grossberg neural networks is investigated. First, the global Mittag-Leffler boundedness is introduced as a new type of boundedness. Based on some fractional-order differential inequalities and Lyapunov functions method, some effective criteria are derived to guarantee such kind of boundedness of the addressed networks under different activation functions. Here, the activation functions are no longer assumed to be derivable which is always demanded in relating references. Meanwhile, the framework of the global Mittag-Leffler attractive sets in the state space is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, two numerical examples with simulations are presented to show the effectiveness of the obtained results.

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Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China under Grant 11601268.

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Authors and Affiliations

  1. College of Science, China Three Gorges University, Yichang, 443002, Hubei, China

    Peng Wan & Jigui Jian

  2. Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, 443002, Hubei, China

    Jigui Jian

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  1. Peng Wan
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Correspondence to Jigui Jian.

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Wan, P., Jian, J. Global Mittag-Leffler Boundedness for Fractional-Order Complex-Valued Cohen–Grossberg Neural Networks. Neural Process Lett 49, 121–139 (2019). https://doi.org/10.1007/s11063-018-9790-z

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  • DOI: https://doi.org/10.1007/s11063-018-9790-z

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