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

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

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

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.

Keywords: Stability; Complete synchronization; Finite-time synchronization; Fractional-order gene regulatory networks; Adaptive control (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923006872

DOI: 10.1016/j.chaos.2023.113786

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