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Speaker: Philippe Jacquod, School of Engineering, Univ of Applied Sciences of Western Switzerland HES-SO
Title: Route to Chaos and Unified Dynamical Framework in Multi-Species Ecosystems
Abstract: One of the main challenges in theoretical ecology is to connect predictions from mathematical models of population dynamics to empirical observations ofspecies coexistence in natural or laboratory-controlled ecosystems. It is not debated that individual populations fluctuate in time, with some populations exhibiting synchronized, periodic oscillations, while others have a seemingly chaotic dynamics. This has to be put in perspective with many theoretical approaches focusing on the time-asymptotic, fixed-point behavior of mathematical models.
In this talk, I will investigate multi-species models of population dynamics. I will emphasize the richness of dynamics of these rather simple models as a function of two key parameters (i) the variability σ of interspecies interactions, and (ii) the off-diagonal covariance parameter γ of the interaction matrix. I will show that, for sufficiently negative γ, the stable fixed-points prevailing at small σ generically lose their stability through Hopf bifurcations. Limit cycles emerge, where surviving species have periodically oscillating abundances. At still stronger interactions, strange attractors appear, which lead to a chaotic dynamics of population abundances. This route to chaos illustrates how stationarity, oscillating periodicity and chaos in the dynamics of species abundances exist in rather general models of population dynamics, depending on σ and γ. One important
result is that all observed population dynamics in multi-species ecosystems can be reproduced by a unified mathematical model.
Talk based on R. Delabays and Ph. Jacquod, arXiv:2503.16999.