Impulsive effects on fractional order time delayed gene regulatory networks: Asymptotic stability analysis

Abstract

This paper address the fractional-order gene regulatory networks (FOGRNs) with both time delays and impulsive effects. Inspired by the integer-order gene regulatory network models, a general class of fractional-order gene regulatory network model is further investigated via fractional-order Lyapunov-Razumikhin stability theory. Firstly, impulsive effects, feedback regulation, and translation time delays are taken well into account and effective analysis techniques are used to reflect the system’s practically dynamic behavior. Secondly, the existence and uniqueness of the equilibrium point of the fractional-order gene regulatory networks are derived based on the Banach contraction mapping principle. Besides, we derived analytically the condition under which the solution of this network is bounded through generalized Gronwall inequality. Thirdly, some novel delay-free sufficient conditions are derived to ensure the global asymptotic stability of the considered model with the help of the fractional-order Lyapunov-Razumikhin method and properties of Mittag-Leffler functions. Finally, an example with numerical simulation is provided to illustrate the validity and effectiveness of the proposed results.