Hybrid control on bifurcation for a delayed fractional gene regulatory network

• Fractional gene regulatory network with time delays is proposed.
• The effect of time delays on the stability for uncontrolled network is studied.
• The influence of fractional order on bifurcation point is discussed.
• Hybrid controller on control bifurcation for uncontrolled network is designed.
• The impact of feedback gain on bifurcation control for controlled network is developed.

A novel delayed fractional-order gene regulatory network model is proposed in this paper. Firstly, the sum of delays is chosen as the bifurcation parameter, the conditions of the existence for the Hopf bifurcation are obtained by analyzing the associated characteristic equation. Then, it is the first time that a hybrid controller is designed to control the Hopf bifurcation for the proposed network. It is demonstrated that both fractional order and feedback gain can effectively control the dynamics of such network, the stability domain can be extended under the small fractional order or feedback gain. The controller is enough to delay the onset of the Hopf bifurcation and achieve some desirable dynamical behaviors by changing the appropriate order or feedback gain. Finally, numerical simulations are employed to justify the validity of our theoretical analysis.