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 tau_{1} and 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.
Highlights
As we know, plants play a vital role in the everyday life of all organisms on earth
In [3], the transmission pathways of plant viruses were analyzed in detail from the perspective of plants and media; the authors established a model of plant infections disease and analyzed the dynamics of the model
When τ1 = 0 and τ2 > 0, the stability of the equilibrium E(S∗, I∗, Y ∗) and the existence of Hopf bifurcation can be obtained based on a similar discussion, which we omit in this paper
Summary
Plants play a vital role in the everyday life of all organisms on earth. Sometimes, plants become infected with a virus, which can have a devastating effect on the ecosystem that depends on it. 2, we study the stability of positive equilibrium and the existence of local Hopf bifurcation of system (1.3). 2 Stability and existence of Hopf bifurcation System (1.3) has a unique positive equilibrium E(S∗, I∗, Y ∗), provided that the following conditions are satisfied: (H1) mω + K μ(β1 + α1m) > dm, αβ1K μ + m(mω + K μ(β1 + α1m) – dm) > 0, β1βK μ > m2μω, αmμω + β(mω + K μ(β1 + α1m) – dm) > 0, where ω(αβ1K β1β (ω μ + m(mω + K μ(β1 + α1m) – dm)) – d) + αβ1 μω + β1mμω + α1m2μω
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