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Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives

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  • Stamov, Gani
  • Stamova, Ivanka
  • Martynyuk, Anatoliy
  • Stamov, Trayan

Abstract

This paper introduces a new class of reaction–diffusion neural networks with impulses and recently defined fractional-like derivatives. Sufficient conditions for the existence-uniqueness of almost periodic solutions are proposed by constructing suitable Lyapunov-like functions. Our results are new and contribute to the development of the knowledge on impulsive fractional-like evolution models. Finally, as an example a fractional-like generalization of a reaction-diffusion model in epidemiology that simulates the hepatitis B virus (HBV) infection with spatial dependence is considered.

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  • Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310389
    DOI: 10.1016/j.chaos.2020.110647
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    References listed on IDEAS

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    1. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
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    7. Hai Zhang & Renyu Ye & Song Liu & Jinde Cao & Ahmad Alsaedi & Xiaodi Li, 2018. "LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 537-545, February.
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    Cited by:

    1. Fei Luo & Weiyi Hu & Enli Wu & Xiufang Yuan, 2024. "Global Exponential Stability of Impulsive Delayed Neural Networks with Parameter Uncertainties and Reaction–Diffusion Terms," Mathematics, MDPI, vol. 12(15), pages 1-15, July.
    2. Abulajiang Aili & Shenglong Chen & Sibao Zhang, 2024. "Event-Triggered Synchronization of Coupled Neural Networks with Reaction–Diffusion Terms," Mathematics, MDPI, vol. 12(9), pages 1-16, May.
    3. Chen, Jing & Xiao, Min & Wu, Xiaoqun & Wang, Zhengxin & Cao, Jinde, 2022. "Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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