| Volume 10, Number 6, 2020, Pages 2711-2721 DOI：10.11948/20200084 |
| Stability and Hopf bifurcation analysis on a spruce-budworm model with delay |
| Lijun Zhang,Jianming Zhang |
| Keywords:Spruce-budworm, Hopf bifurcation, normal form, center manifold. |
| Abstract: |
| In this paper, the dynamics of a spruce-budworm model with delay is investigated. We show that there exists Hopf bifurcation at the positive equilibrium as the delay increases. Some sufficient conditions for the existence of Hopf bifurcation are obtained by investigating the associated characteristic equation. By using the theory of normal form and center manifold, explicit expression for determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are presented. |
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