Bistability and local bifurcation of delayed gene regulatory network
LAI Qiang1， HUANG Jianning2
1.School of Electrical and Automation Engineering， East China Jiaotong University， Nanchang 330013， China；2.Department of Basic Sciences， Nanchang University College of Science and Technology， Nanchang 330029， China
Abstract：This paper investigates the bistability and local bifurcation of delayed gene regulatory network with three nodes and two feedback loops. The existence of positive equilibrium point of the network is determined. By analyzing the corresponding characteristic equation， the existence conditions of the bistability and Hopf bifurcation the network have been obtained. It shows that the network may perform bistability when the network has positive feedback loop， and Hopf bifurcation will appear when the network has negative feedback loop and the time delay passes a critical value. Numerical simulations illustrate the correctness of our theoretical results.
2018, Vol. 52 
