Global Bifurcation of Positive Equilibria in Nonlinear Population Models

TL;DR

This paper investigates the existence and bifurcation of positive equilibrium solutions in age-structured nonlinear population models, demonstrating global bifurcation phenomena and establishing existence results using fixed point theorems.

Contribution

It introduces a global bifurcation analysis for positive equilibria in nonlinear population models with age structure and nonlinear diffusion, extending previous local results.

Findings

Global bifurcation of positive equilibria from trivial solutions

Existence of positive equilibria in parameter-independent models

Application of fixed point theorems to establish solutions

Abstract

Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive equilibria by means of a fixed point theorem for conical shells.