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

Jixun Chu, Arnaud Ducrot, Pierre Magal, Shigui Ruan

Research output: Contribution to journalArticle

26 Citations (Scopus)

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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Population dynamics
Structured Populations
Hopf bifurcation
Population Model
Population Dynamics
Hopf Bifurcation
Dynamic models
Dynamic Model
Semilinear Equations
Integrated Semigroups
Age-structured Model
Center Manifold Theorem
Nonlocal Boundary Conditions
Center Manifold
Growth Process
Nonlinear Boundary Conditions
Reaction-diffusion Equations
Model
Fluctuations
Boundary conditions

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Hopf bifurcation in a size-structured population dynamic model with random growth. / Chu, Jixun; Ducrot, Arnaud; Magal, Pierre; Ruan, Shigui.

In: Journal of Differential Equations, Vol. 247, No. 3, 01.08.2009, p. 956-1000.

Research output: Contribution to journalArticle

Chu, Jixun ; Ducrot, Arnaud ; Magal, Pierre ; Ruan, Shigui. / Hopf bifurcation in a size-structured population dynamic model with random growth. In: Journal of Differential Equations. 2009 ; Vol. 247, No. 3. pp. 956-1000.
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