In dynamical systems, an equilibrium is said to be stable if the system is dynamically brought back to it after some perturbations. In other words, a system is destabilized if it escapes the basin of attraction of its initial equilibrium. Determining conditions guaranteeing that the system remains in its initial basin of attraction is then important for many practical applications. One example among others being electrical networks, which are subject to increasingly fluctuating power injections, due to the ongoing energy transition. In this context, we will see a simple analytical method to assess the time needed for a network of coupled oscillators subject to noise to leave its initial basin of attraction. This estimate can easily be computed for a given network as it relies on: (i) characteristics of the network, namely the inertia and damping of the oscillators and most importantly the underlying interaction graph; (ii) the noise's parameters, namely its amplitude and its correlation time; (iii) the size of the basin of attraction. Interestingly, according to this estimate and to simulations, increasing the amount of intertia reduces the time needed for the system of escape its initial basin of attraction, reducing then the stability of the corresponding equilibrium.
Robin obtained his master degree in Mathematics at the University of Geneva in 2014. He then did his PhD at the University of Applied Sciences of Western Switzerland (HES-SO) in Sion, in the middle of the Swiss Alps. His research focusses on synchronization of networks of coupled oscillators, and more specifically on the Kuramoto model. He is currently a postdoc associate, sharing his time between HES-SO and ETH Zürich.