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Stability and bifurcations in fractional-order gene regulatory networks

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  • Kaslik, Eva
  • Rădulescu, Ileana Rodica

Abstract

A fractional-order mathematical model of a large-scale GRN is presented, focusing on the positivity of solutions and on the stability analysis of equilibria based on Matignon’s theorem. With special emphasis on cyclic GRNs, necessary and sufficient conditions are obtained in terms of inequalities involving the system’s parameters and the fractional order, which guarantee the stability of equilibrium points. Based on the stability analysis, the critical values of the fractional order for which Hopf-type bifurcations may occur are detected. In this context, it is shown that oscillatory behavior due to a Hopf-type bifurcation (considering the fractional order as bifurcation parameter) is expected only in the case of an odd number of repressive genes. Numerical examples are given in order to demonstrate the usefulness of the proposed results and to exemplify the effect of the fractional order on the dynamics of cyclic GRNs, additionally revealing that period-doubling bifurcations of limit cycles may also occur in sufficiently large cyclic GRNs.

Suggested Citation

  • Kaslik, Eva & Rădulescu, Ileana Rodica, 2022. "Stability and bifurcations in fractional-order gene regulatory networks," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000029
    DOI: 10.1016/j.amc.2022.126916
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    References listed on IDEAS

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    Cited by:

    1. Chen, Shenglong & Yang, Jikai & Li, Zhiming & Li, Hong-Li & Hu, Cheng, 2023. "New results for dynamical analysis of fractional-order gene regulatory networks with time delay and uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. 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).

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