Linearized stability of structured population dynamical models

Linearized stability of structured population dynamical models Selected results from the thesis

Dynamical behavior of a stage structured prey-predator model

In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to ob...

On the Linearized Stability of Age-structured Multispecies Populations

In [13] Prüß investigated a very general nonlinear age-structured model consisting of n species. He proved the principle of linearized stability, which means that the asymptotic behavior of stationary solutions of the nonlinear system is determined by the spectrum of the linearized operator. In other words the stability is determined by the roots of a complex valued characteristic function as i...

Asymptotic behavior of size structured populations via juvenile-adult interaction∗

In this work a size structured juvenile-adult population model is considered. The linearized dynamical behavior of stationary solutions is analyzed using semigroup and spectral methods. The regularity of the governing linear semigroup allows to derive biologically meaningful conditions for the linear stability of stationary solutions. The main emphasis in this work is on juvenile-adult interact...

(bi)stability and the Net Growth Rate

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 linearized system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net re...