Abstract:Année de publication : 2021
This thesis is a mathematical study of ecological models. The setup is the following: assume we delimit some forest parcel, and reference the populations of the various species it contains. If we let the ecosystem be, some species will bloom, oth- ers will go extinct. Our mathematical model predicts how the populations will change with time. In this PhD, we focus more specically on the chaotic dynamics. In plain words, if whenever we go back to the forest parcel, the populations are dierent (sometimes the most abundant species is the rabbits, sometimes the boars), we will call this ecosystem chaotic. Usu- ally in ecology, chaotic dynamics in isolated ecosystems are discarded, because they are un- stable. In this work, we try to convey that chaotic dynamics are quite resilient. To do so, we introduce a specic mathematical tool. Then we perform various studies, both from pure mathematics and computer simulations, to show that lasting chaotic behaviour emerges.