Authors: József Z Farkas
Publish Date: 2010/02/09
Volume: 35, Issue: 1-2, Pages: 617-633
Abstract
We consider a class of physiologically structured population models a first order nonlinear partial differential equation equipped with a nonlocal boundary condition with a constant external inflow of individuals We prove that the linearised system is governed by a quasicontraction semigroup We also establish that linear stability of equilibrium solutions is governed by a generalised net reproduction function In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero ie when linearisation does not decide stability This allows us to demonstrate through a concrete example how immigration might be beneficial to the population In particular we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates In fact the linearised system exhibits bistability for a certain range of values of the external inflow induced potentially by Alléeeffect
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