Models of population dynamics under the influence of external perturbations: mathematical results

TL;DR

This paper analyzes how external perturbations affect population dynamics modeled by a reaction-diffusion equation, providing mathematical insights into equilibrium states and long-term behavior, with implications for sustainable yields.

Contribution

It offers a mathematical framework linking external forcing to population equilibrium and asymptotic behavior, simplifying the analysis of time-periodic effects.

Findings

Asymptotic behavior reduces to autonomous case analysis

Stationary equilibria depend on external perturbation size

Numerical computations illustrate sustainable yield implications

Abstract

In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the asymptotic behaviour in the time-periodic forcing case can be reduced to the autonomous one, the last one being described in function of the "size" of the external perturbation. Our results can be interpreted in terms of maximal sustainable yields from populations. We briefly discuss this last aspect through a numerical computation.