Multiple Equilibria, Aging Dynamics and Chaos in Large Interacting Ecosystems
Giulio Biroli (LPENS)
I will focus on Lotka-Volterra equations, which provide a general model to study large assemblies of strongly interacting degrees of freedom in many different fields: biology, economy and in particular ecology. I will present our analysis of the generalised Lotka-Volterra model of an ecological community formed by a large number of species and focus in particular on two different phases that emerge: when interactions are symmetric we find a regime, akin to the spin-glass phase of random magnets, characterized by an exponential number of multiple equilibria, all poised at the edge of stability. For non-symmetric interactions, this phase is replaced by a chaotic one or a dynamical aging regime depending on the presence of immigration from the mainland. Finally, I will consider spatially coupled communities and show that migration between them plays a key role in enhancing chaos and diversity of the ecosystem.