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Bifurcation analysis of a spruce budworm model with diffusion and physiological structures. (English) Zbl 1361.35186

Summary: In this paper, the dynamics of a spruce budworm model with diffusion and physiological structures are investigated. The stability of steady state and the existence of Hopf bifurcation near positive steady state are investigated by analyzing the distribution of eigenvalues. The properties of Hopf bifurcation are determined by the normal form theory and center manifold reduction for partial functional differential equations. And global existence of periodic solutions is established by using the global Hopf bifurcation result of Wu. Finally, some numerical simulations are carried out to illustrate the analytical results.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
35B32 Bifurcations in context of PDEs
35B10 Periodic solutions to PDEs
35B35 Stability in context of PDEs
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