New exploration on bifurcation in fractional-order genetic regulatory networks incorporating both type delays

This study principally deals with the stability property and the emergence of Hopf bifurcation for fractional-order genetic regulatory networks incorporating distributed delays and discrete delays. By two suitable variable substitutions, we obtain two new equivalent fractional-order differential systems involving only discrete delay. Applying the stability technique and bifurcation theory of fractional-order differential equations, we set up two new sufficient criteria guaranteeing the stability and the generation of Hopf bifurcation of the involved fractional-order genetic regulatory network models. The research confirms that the delay has a momentous influence on the stability of networks and bifurcation control for the considered fractional-order genetic regulatory networks. The Matlab simulation plots effectively check the effectiveness of the theoretical analysis. The established results of this research can be powerfully utilized to control genetic regulatory networks and owns very useful theoretical value in life activities.