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Preprints, Working Papers, ... Year : 2015

Analysis of a time-dependent problem of mixed migration and population dynamics

Abstract

In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other through a Lotka-Volterra term. These two contributions naturally induce two separated time-scales in the problem. A generalized center manifold theorem is derived to handle the situation where the linear terms are depending on the fast time in a periodic way. The resulting equations are then amenable to averaging methods. As a product of these combined techniques, one obtains an autonomous differential system in reduced dimension whose dynamics can be analyzed in a much simpler way as compared to original equations. Strikingly enough, this system is of Lotka-Volterra form with modified coefficients. Besides, a higher order perturbation analysis allows to show that the oscillations on the original model destabilize the cycles of the averaged Volterra system in a way that can be explicitely computed.

Dates and versions

hal-01255118 , version 1 (13-01-2016)

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François Castella, Philippe Chartier, Julie Sauzeau. Analysis of a time-dependent problem of mixed migration and population dynamics. 2015. ⟨hal-01255118⟩
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