Novel Nonlinear Control for a Class of Non-Integer Order Time Lag Gene System

This study presents the bifurcation analysis and stabilization via the impulsive control of a fractional-order gene regulatory network with time delay. First, the author chooses the transcription rate k as the bifurcation parameter and obtains the Hopf bifurcation condition by analyzing its characteristic equation. The research shows that Hopf bifurcation occurs when the transcription rate k exceeds a critical value. This bifurcation behavior may destabilize the system. Subsequently, the author designs an impulsive controller to stabilize the system. Finally, simulation examples are used to verify our theory.