Stability and Hopf Bifurcation Control for Fractional-Order Two-Gene Regulatory Network With Multiple Delays

Abstract

The study of dynamic behavior can better understand the mechanism of genetic regulatory network. DNA is transcribed into mRNA and mRNA is translated into proteins. The process takes time to complete. A four-dimensional fractional-order two-gene regulatory network with multiple delays is studied in this paper. Firstly, the characteristic equation at the positive equilibrium is given. Secondly, choosing two delays as bifurcation parameters, we calculate the stability switching curves in the delay plane and get the conditions for the existence of Hopf bifurcation. When genetic regulatory network appeared periodic solution, we introduce fractional-order proportional-derivative (PD) controller to control the stability of the two-gene regulatory network. Finally, the correctness of the theoretical analysis is illustrated by numerical simulation. The results show that the stable region of the genetic regulatory network can be expanded or reduced by changing delays or two parameters of fractional-order PD controller. The fractional-order PD controller can effectively control Hopf bifurcation of genetic regulatory network.

Keywords

• Two-gene regulatory network
• multiple delays
• fractional-order PD controller
• stability switching curves
• Hopf bifurcation