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Stability analysis for a class of impulsive competitive neural networks with leakage time-varying delays

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Abstract

In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer’s fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.

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Authors and Affiliations

  1. Faculty of Sciences of Bizerta, Department of Mathematics, Research Units of Mathematics and Applications, UR13ES47, University of Carthage, Bizerta, 7021, Tunisia

    Chaouki Aouiti & El Abed Assali

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    JinDe Cao

  3. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    JinDe Cao

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

Authors
  1. Chaouki Aouiti
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  2. El Abed Assali
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  3. JinDe Cao
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  4. Ahmed Alsaedi
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Correspondence to Chaouki Aouiti.

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Aouiti, C., Assali, E.A., Cao, J. et al. Stability analysis for a class of impulsive competitive neural networks with leakage time-varying delays. Sci. China Technol. Sci. 61, 1384–1403 (2018). https://doi.org/10.1007/s11431-017-9163-7

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  • DOI: https://doi.org/10.1007/s11431-017-9163-7

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