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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:
      The dynamics of a spruce-budworm model with delay are investigated in this paper. We show that Hopf bifurcations occur at the positive equilibrium when the delay increases. Sufficient conditions for the existence of Hopf bifurcation are examined 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 stability of bifurcating periodic solutions are obtained.