Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

Abstract

This paper investigates the problem of bifurcation analysis and bifurcation control of a fractional-order gene regulatory network with sRNA. Firstly, the process of stability change of system equilibrium under the influence of the sum of time delay is discussed, the critical condition of Hopf bifurcation is explored, and the effect of fractional order on the system stability domain. Secondly, aiming at the system’s instability caused by a large time delay, we design a controller to improve the system’s stability and derive the parameter conditions that satisfy the system’s stability. It is found that changing the parameter values of the controller within a certain range can control the system’s nonlinear behaviours and effectively expand the stability range. Then, a numerical example is given to illustrate the results of this paper.