A Nonlinear Logistic Model for Age-Structured Populations: Analysis of Long-Term Dynamics and Equilibria

TL;DR

This paper develops a nonlinear logistic model for age-structured populations, analyzing long-term behavior and equilibria, with theoretical results on existence and uniqueness of solutions, aiding demographic modeling.

Contribution

It introduces a novel nonlinear logistic framework for age-structured populations, providing new theoretical insights into equilibrium conditions and long-term dynamics.

Findings

Conditions for existence of equilibria established

Uniqueness of stationary solutions proven

Insights into asymptotic population behavior obtained

Abstract

This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and asymptotic behavior. Theoretical findings establish conditions for the existence and uniqueness of equilibrium solutions and explore long-term population dynamics. This study provides valuable tools for demographic modeling and opens avenues for further mathematical exploration.