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

Research paper by Mickaël D. Chekroun, Lionel Roques

Indexed on: 13 Jun '10Published on: 13 Jun '10Published in: Mathematics - Analysis of PDEs



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.