Highly oscillating center manifold and an application in ecology

Abstract : We have studied a differential system ruled by two dynamics : a center manifold dynamics and a periodic highly oscillating dynamics. We wanted to find informations about the qualitative behaviour of the system, and to approximate it. We have proved the existence of a highly oscillating asymptotic dynamics, and we have used it approximate the system. Then, we have applied this results to an ecological system of prey-predator interaction. Moreover, we have used the B-series theory to obtain formal expansions of the quantities related to the center manifold. Lastly, we have approximated the system for all time by the composition of a change of variable and of the solution of a partially decoupled differential system.
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Julie Sauzeau. Highly oscillating center manifold and an application in ecology. Dynamical Systems [math.DS]. Université Rennes 1, 2016. English. ⟨NNT : 2016REN1S018⟩. ⟨tel-01382775⟩

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