Assessing the complexity of large interacting ecosystems through the lens of random matrix theory

par Ada Altieri (Université Paris Cité)

mercredi 6 sept. 2023, 14:00 → 15:00 Europe/Paris

https://greenlight.virtualdata.cloud.math.cnrs.fr/b/fab-49u-gkt

Many complex systems in Nature — from metabolic networks to ecosystems — appear to be poised at the edge of stability, hence displaying enormous responses to external perturbations. This marginal stability condition is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics, and therefore critical behaviors.
   I will introduce the large-dimensional version of the Generalized Random Lotka-Volterra model with demographic noise and immigration. Leveraging on techniques rooted in the theory of spin glasses and random matrices, I will unveil a very rich — eventually hierarchical — structure in the organization of the equilibria and relate the slowing down of correlation functions to glassy-like properties. 
   Finally, I will discuss extensions to non-logistic growth functions allowing for the description of positive feedback mechanisms as well as for the detection of novel phases as a smoking-gun signature of criticality.