Counting equilibria in complex systems via random matrices

Abstract

How many equilibria will a large complex system, modeled by N randomly coupled autonomous nonlinear differential equations typically have? How many of those equilibria are stable, that is are local attractors of the nearby trajectories? These questions arise in many applications and can be partly answered by employing the methods of Random Matrix Theory. The lectures will outline these recent developments. Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom E-mail address: yan.fyodorov@kcl.ac.uk c ©2017 American Mathematical Society