首页|Stability and bifurcations in fractional-order gene regulatory networks

Stability and bifurcations in fractional-order gene regulatory networks

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  • NSTL
  • Elsevier
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. (C) 2022 Elsevier Inc. All rights reserved.

Gene regulatory networkAsymptotic stabilityHopf bifurcationPeriod doublingOscillatory behaviorFractional-order differential equationsCaputo derivativeHOPF-BIFURCATIONNUMERICAL-SOLUTIONMODELOSCILLATIONSEXPRESSIONCRITERIONSYSTEMSDELAYSFATE

Kaslik, Eva、Radulescu, Ileana Rodica

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West Univ Timisoara

Univ Politehn Bucuresti

2022

10.1016/j.amc.2022.126916

Applied mathematics and computation

Applied mathematics and computation

EISCI
ISSN：0096-3003
年,卷(期)：2022.421
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