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Stability of Traveling Waves Solutions for Nonlinear Cellular Neural Networks with Distributed Delays

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Abstract

This paper investigates the exponential stability of traveling wave solutions for nonlinear delayed cellular neural networks. As a continuity of the past work (Wu and Niu, 2016; Yu, et al., 2011) on the existence and uniqueness of the traveling wave solutions, it is very reasonable and interesting to consider the exponential stability of the traveling wave solutions. By the weighted energy method, comparison principle and the first integral mean value theorem, this paper proves that, for all monotone traveling waves with the wave speed \(c < c_1^ \ast < 0\) or \(c > c_2^ \ast > 0\), the solutions converge time-exponentially to the corresponding traveling waves, when the initial perturbations decay at some fields.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Yingxin Guo

  2. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Singapore

    Shuzhi Sam Ge

  3. National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, El Khawarizmi Street, Carthage, 2078, Tunisia

    Adnène Arbi

  4. Laboratory of Engineering Mathematics (LR01ES13), Tunis, Tunisia

    Adnène Arbi

Authors
  1. Yingxin Guo
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  2. Shuzhi Sam Ge
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  3. Adnène Arbi
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Corresponding authors

Correspondence to Yingxin Guo, Shuzhi Sam Ge or Adnène Arbi.

Additional information

This research was supported by the Natural Science Foundation of Shandong Province under Grant No. ZR2017MA045 and the National Natural Science Foundation of China under Grant No. 61873144.

This paper was recommended for publication by Editor WU Zhengguang.

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Guo, Y., Ge, S.S. & Arbi, A. Stability of Traveling Waves Solutions for Nonlinear Cellular Neural Networks with Distributed Delays. J Syst Sci Complex 35, 18–31 (2022). https://doi.org/10.1007/s11424-021-0180-7

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  • DOI: https://doi.org/10.1007/s11424-021-0180-7

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