Stability Analysis and Bifurcation Control of a Delayed Incommensurate Fractional-Order Gene Regulatory Network

Abstract

In this paper, stability analysis and bifurcation control for a novel incommensurate fractional-order delayed gene regulatory network are investigated. Firstly, the associated characteristic equation is analyzed by taking time delay as a bifurcation parameter, and the conditions of creation for Hopf bifurcation are established. It is demonstrated that the time delay can profoundly affect the dynamics of the proposed system and each order has a significant influence on the creation of bifurcation simultaneously. Then we study the stability and bifurcation behavior of the fractional-order networks by adding a nonlinear feedback controller. Finally, numerical simulations of two examples validate the obtained results.