Hopf bifurcation in a size-structured population dynamic model with random growth

Jixun Chu, Arnaud Ducrot, Pierre Magal, Shigui Ruan

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Abstract

This paper is devoted to the study of a size-structured model with Ricker type birth function as well as random fluctuation in the growth process. The complete model takes the form of a reaction-diffusion equation with a nonlinear and nonlocal boundary condition. We study some dynamical properties of the model by using the theory of integrated semigroups. It is shown that Hopf bifurcation occurs at a positive steady state of the model. This problem is new and is related to the center manifold theory developed recently in [P. Magal, S. Ruan, Center manifold theorem for semilinear equations with non-dense domain and applications to Hopf bifurcation in age-structured models, Mem. Amer. Math. Soc., in press] for semilinear equation with non-densely defined operators.

Original languageEnglish (US)
Pages (from-to)956-1000
Number of pages45
JournalJournal of Differential Equations
Volume247
Issue number3
DOIs
StatePublished - Aug 1 2009

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Keywords

  • Hopf bifurcation
  • Integrated semigroups
  • Population dynamics
  • Size structure

ASJC Scopus subject areas

  • Analysis

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