Asymptotic behavior of bifurcation curves of nonlocal logistic equation of population dynamics

TL;DR

This paper analyzes the asymptotic behavior of bifurcation curves in a nonlocal logistic population model, providing precise formulas as the solution norm grows large, enhancing understanding of population dynamics in nonlocal frameworks.

Contribution

It establishes exact asymptotic formulas for bifurcation curves in a nonlocal logistic equation, a novel contribution to the mathematical analysis of population models.

Findings

Derived asymptotic formulas for bifurcation curves as solution norm increases

Enhanced understanding of nonlocal logistic population dynamics

Mathematical characterization of bifurcation behavior in nonlocal models

Abstract

We study the one-dimensional nonlocal Kirchhoff type bifurcation problem related to logistic equation of population dynamics. We establish the precise asymptotic formulas for bifurcation curve $\lambda = \lambda(\alpha)$ as $\alpha \to \infty$ in $L^2$-framework, where $\alpha:= \Vert u_\lambda \Vert_2$.