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Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models

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  • Stamova, Ivanka
  • Stamov, Trayan
  • Stamov, Gani

Abstract

In this paper, the concept of Lipschitz stability is introduced to impulsive delayed reaction-diffusion neural network models of fractional order. Such networks are an appropriate modeling tool for studying various problems in engineering, biology, neuroscience and medicine. Fractional derivatives of Caputo type are considered in the model. The effects of impulsive perturbations and delays are also under consideration. Lipschitz stability analysis is performed and sufficient conditions for global uniform Lipschitz stability of the model are established. The Lyapunov function approach combined with the comparison principle are employed in the development of the main results. The proposed criteria extend some existing stability results for such models to the Lipschitz stability case. The introduced concept is also very useful in numerous inverse problems.

Suggested Citation

  • Stamova, Ivanka & Stamov, Trayan & Stamov, Gani, 2022. "Lipschitz stability analysis of fractional-order impulsive delayed reaction-diffusion neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006841
    DOI: 10.1016/j.chaos.2022.112474
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    References listed on IDEAS

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    1. Gani Stamov & Ivanka Stamova & George Venkov & Trayan Stamov & Cvetelina Spirova, 2020. "Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
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    5. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.
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    Cited by:

    1. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    2. Xie, Xiang & Li, Xiaodi & Liu, Xinzhi, 2023. "Event-triggered impulsive control for multi-agent systems with actuation delay and continuous/periodic sampling," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Yang, Dongsheng & Yu, Yongguang & Wang, Hu & Ren, Guojian & Zhang, Xiaoli, 2024. "Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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