Analysis and State Feedback Control Bifurcation of Fractional -Order Cyclic Gene Regulatory Networks with Time Delay

In this paper, a fractional-order cyclic gene regulatory network model with time delay is studied. Firstly, the total time delay of the system is selected as the bifurcation parameter, and the condition for the existence of Hopf bifurcation is derived by analyzing its characteristic equation. It is found that the time delay affects the stability of the system, and the order affects the position of the bifurcation point. When the time delay is greater than the critical time delay, the system loses stability. Secondly, a state feedback controller is designed for the unstable system. It is proved that the control method has good control effect for the system instability caused by Hopf bifurcation. Finally, the correctness of the theoretical derivation is verified by simulation.