Hopf bifurcation of a delayed single population model with patch structure

2019/12/26 by Shanshan Chen, Chen, Shanshan, Zuolin Shen +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1912.11780

openalex publication_date 2019/12/26 · openalex created_date 2020/01/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show the existence of Hopf bifurcation of a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we show that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the "local" Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the "average" model.

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