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Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks

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  • Yang, Juanping
  • Sheng, Yuhong
  • Li, Hong-Li
  • Hu, Cheng

Abstract

This paper is devoted to investigating stability and synchronization issues for delayed uncertain fractional-order gene regulatory networks (DUFOGRNs). First, the existence and uniqueness of the equilibrium point of the DUFOGRNs are explored via constructing contraction map, whereafter, a stability criterion is studied by means of the fractional-order Lyapunov–Razumikhin approach and property of Mittag-Leffler function. Second, a novel fractional-order Lemma is established by using the theory of fractional calculus showing that the derivative of Lyapunov functions in the fractional-order systems (FOSs) satisfy certain form of convergence, which can be able to discuss the problems about finite-time stability and synchronization of FOSs. Third, adaptive control strategies are designed based on the established Lemma, which are different control protocols anent the synchronization of gene regulatory networks proposed in previous work. Furthermore, sufficient synchronization criteria are derived by probing fractional calculus theory and inequality analysis techniques for guaranteeing the complete synchronization (CS) and finite-time synchronization (F-TS) of DUFOGRNs. Finally, three numerical examples are provided to verify the availability of the proposed method.

Suggested Citation

  • Yang, Juanping & Sheng, Yuhong & Li, Hong-Li & Hu, Cheng, 2023. "Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006872
    DOI: 10.1016/j.chaos.2023.113786
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    References listed on IDEAS

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    1. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    2. Huang, Chengdai & Cao, Jinde & Xiao, Min, 2016. "Hybrid control on bifurcation for a delayed fractional gene regulatory network," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 19-29.
    3. Kaslik, Eva & Rădulescu, Ileana Rodica, 2022. "Stability and bifurcations in fractional-order gene regulatory networks," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    4. Zang, Hong & Zhang, Tonghua & Zhang, Yanduo, 2015. "Bifurcation analysis of a mathematical model for genetic regulatory network with time delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 204-226.
    5. Attila Becskei & Luis Serrano, 2000. "Engineering stability in gene networks by autoregulation," Nature, Nature, vol. 405(6786), pages 590-593, June.
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