Hopf bifurcation analysis for a model of plant virus propagation with two delays

Abstract

Abstract In this paper, we consider a model of plant virus propagation with two delays and Holling type II functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are analyzed by choosing τ1 $\tau_{1}$ and τ2 $\tau_{2}$ as bifurcation parameters, respectively. Using the center manifold theory and normal form method, we discuss conditions for determining the stability and the bifurcation direction of the bifurcating periodic solution. Finally, we carry out numerical simulations to illustrate the theoretical analysis.

Keywords

• Delay differential equation
• Virus propagation
• Hopf bifurcation
• Holling type II