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Global Mittag-Leffler Stability of Fractional Hopfield Neural Networks with δ-Inverse Hölder Neuron Activations

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Abstract

In this paper, the global Mittag-Leffler stability of fractional Hopfield neural networks (FHNNs) with \(\delta \)-inverse hölder neuron activation functions are considered. By applying the Brouwer topological degree theory and inequality analysis techniques, the proof of the existence and uniqueness of equilibrium point is addressed. By constructing the Lure’s Postnikov-type Lyapunov functions, the global Mittag-Leffler stability conditions are achieved in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are given to verify the validity of the theoretical results.

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Authors and Affiliations

  1. School of Science, Yanshan University, 066001, Qinhuangdao, China

    Xiaohong Wang &  Huaiqin Wu

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  1. Xiaohong Wang
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  2. Huaiqin Wu
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Correspondence to Xiaohong Wang or Huaiqin Wu.

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Xiaohong Wang, Huaiqin Wu Global Mittag-Leffler Stability of Fractional Hopfield Neural Networks with δ-Inverse Hölder Neuron Activations. Opt. Mem. Neural Networks 28, 239–251 (2019). https://doi.org/10.3103/S1060992X19040064

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  • DOI: https://doi.org/10.3103/S1060992X19040064

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