Positive Equilibrium Solutions for Age and Spatially Structured Population Models

TL;DR

This paper investigates the existence of positive equilibrium solutions in age-structured population models with nonlinear diffusion, demonstrating bifurcation from trivial equilibria as fertility intensity varies.

Contribution

It introduces a bifurcation analysis framework for age and space-structured population models with nonlinear diffusion, identifying conditions for positive equilibria.

Findings

Positive equilibrium solutions bifurcate from trivial solutions as fertility increases.

The direction of bifurcation is analyzed in specific cases.

A bifurcation parameter related to fertility controls the emergence of equilibria.

Abstract

The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility it is shown that a branch of (positive) equilibria bifurcates from the trivial equilibrium. In some cases the direction of bifurcation is analyzed.