Hopf Bifurcation Control of Single-gene Expression Models with Two Delays via State Feedback

In this paper, we propose a state feedback method to control the Hopf bifurcation for a single-gene expression model. We choose the sum of the delays as the bifurcation parameter. Without control, the bifurcation will occur early when the sum of the delays passes through a certain value. However, under the control of the state feedback, the onset of the critical value of the undesirable Hopf bifurcation is postponed, and thus the model can remain stable for a larger delay. Finally, through the numerical simulations we verify the correctness of the theoretical results