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\(\alpha \)-Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays

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Abstract

This paper investigates the global \(\alpha \)-exponential stability of impulsive fractional-order complex-valued neural networks with time delays. By constructing proper Lyapunov–Krasovskii functional and employing fractional-order complex-valued differential inequality, some sufficient conditions are obtained to ensure the existence, uniqueness and global \(\alpha \)-exponential stability of the equilibrium point for the considered neural networks. Moreover, the exponential convergence rate is estimated, which depends on the parameters and the order of differentiation of system. Finally, one numerical example with simulations is given to illustrate 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 (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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  2. Jigui Jian
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Correspondence to Jigui Jian.

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Wan, P., Jian, J. \(\alpha \)-Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays. Neural Process Lett 50, 1627–1648 (2019). https://doi.org/10.1007/s11063-018-9938-x

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