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Hopf bifurcation in a size-structured population dynamic model with random growth
- Source :
-
Journal of Differential Equations . Aug2009, Vol. 247 Issue 3, p956-1000. 45p. - Publication Year :
- 2009
-
Abstract
- 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 247
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 40121053
- Full Text :
- https://doi.org/10.1016/j.jde.2009.04.003