RESILIENCE IN LARGE RANDOM COMPLEX SYSTEMS - SIRIO BELGA FEDELI - PhD student at King’s College London
In this talk we will extend the highly influential May’s model  for randomly assembled ecological systems, beyond the linear approximation around a given point of equilibrium. We will introduce a generic nonlinear model, in which all higher-order terms in the expansion around the chosen point of equilibrium (placed at the origin) are included with random Gaussian coefficients. As the size of the system grows, in correspondence of the known sharp instability-to-stability transition, the evaluation of the mean number of equilibrium points surrounding the origin reveals the emergence of a “resilience gap”. Namely, there exists a radius r* such that the system is expected to be resilient to a typical initial displacement r«r*. Beyond this radius the phase space is studded by an exponential number of equilibrium points which force the system to wander away from the origin with high probability.
This talk is based on a joint work with Yan Fyodorov(KCL) and Jesper Ipsen(UniMelb):
 R. M. May. "Will a large complex system be stable?" Nature 238 413–414 (1972).
Biography Sirio Belga Fedeli is a PhD student in Applied Mathematics at King’s College London, with deep interests in Random Matrix, Applied Mathematics and Statistical Physics. In 2016 he received a master degree in Mathematical Engineering at Politecnico di Torino, while in 2017 he received a master degree in Science of Non-Equilibrium Physics from King’s College London.