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

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

2010-06-13

arxiv.org/abs/1006.2574v1

Comptes Rendus de l'Acad\'emie des Sciences, Paris, Ser. I (2006), 343: 307--310

Mathematics

Analysis of PDEs

Scientific paper

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.

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