Bifurcation Analysis of a Size-Structured Population Model

Abstract

In this paper, a size-structured population model is studied. Choosing the coefficient of birth function as the varying parameter, we prove the existence of Hopf bifurcation and discuss the bifurcation properties, such as the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. The methods used in this paper include Hopf bifurcation theorem, center manifold theorem and normal form theory for the abstract Cauchy problems in a nondense domain. Numerical simulations are finally carried out to show the theoretical results.