# Seminars & Colloquia Calendar

## Multiple Equilibria and Resilience in Large Complex Systems: beyond May-Wigner model

#### Yan Fyodorov - Kingâ€™s College London

Location: ** zoom**

Date & time: Wednesday, 21 April 2021 at 10:45AM - 11:45AM

Title: Multiple Equilibria and Resilience in Large Complex Systems: beyond May-Wigner model.

I will discuss two different models of randomly coupled N>>1 autonomous differential equations with the aim of counting their fixed points (aka equilibria), and classifying them by their ''instability index'', i.e. the number of unstable directions. In the first model ( studied in a joint paper with G. Ben Arous & B. Khoruzhenko) characterized by both translational and rotational statistical symmetry of the vector field, we estimate the probability of an equilibrium to have a given index in a phase with exponentially many equilibria. In the second model (studied with S. Belga Fedeli & J. Ipsen) characterized by only rotational statistical symmetry around a chosen stable equilibrium, we find a characteristic distance beyond which the multitude of equilibria prevents a trajectory to go towards the stable equilibrium. This may help to shed some light on ''resilience'' mechanisms of complex ecosystems.

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