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Passivity of fractional reaction-diffusion systems

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  • Cao, Yan
  • Zhou, Wei-Jie
  • Liu, Xiao-Zhen
  • Wu, Kai-Ning

Abstract

This study considers the passivity of fractional reaction-diffusion systems (FRDSs) featuring boundary input-output. The fundamental framework for this exploration involves the application of the Lyapunov-Krasovskii functional method coupled with inequality techniques. The investigation derives sufficient conditions that guarantee both input and output strict passivity in FRDSs. Furthermore, in the presence of fluctuating uncertain parameters within FRDSs, robust passivity is also studied and sufficient conditions are offered. The obtained sufficient condition shows that a larger diffusion coefficient facilitates the achievement of the passivity of FRDSs. Finally, the validity of our theoretical findings is subsequently corroborated through numerical examples.

Suggested Citation

  • Cao, Yan & Zhou, Wei-Jie & Liu, Xiao-Zhen & Wu, Kai-Ning, 2024. "Passivity of fractional reaction-diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    • Handle: RePEc:eee:apmaco:v:476:y:2024:i:c:s0096300324002327
    DOI: 10.1016/j.amc.2024.128764
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    References listed on IDEAS

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    1. Liping Chen & Tingting Li & YangQuan Chen & Ranchao Wu & Suoliang Ge, 2019. "Robust passivity and feedback passification of a class of uncertain fractional-order linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(6), pages 1149-1162, April.
    2. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Wang, Yuxiao & Cao, Yuting & Guo, Zhenyuan & Wen, Shiping, 2020. "Passivity and passification of memristive recurrent neural networks with multi-proportional delays and impulse," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Qiu, Hongling & Cao, Jinde & Liu, Heng, 2023. "Passivity of fractional-order coupled neural networks with interval uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 845-860.
    5. Shafiya, M. & Nagamani, G., 2022. "New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    7. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
    8. Yan, Donglin & Wang, Weiyu & Chen, Qijuan, 2020. "Fractional-order modeling and nonlinear dynamic analyses of the rotor-bearing-seal system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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