On the location and the strength of controllers to desynchronize coupled Kuramoto oscillators

Abstract

Synchronization is an ubiquitous phenomenon in dynamical systems of networked oscillators. While it is often a goal to achieve, in some context one would like to decrease it, e.g., although synchronization is essential to the good functioning of brain dynamics, hyper-synchronization can induce problems like epilepsy seizures. Motivated by this problem, scholars have developed pinning control schemes able to decrease synchronization in a system. Focusing on one of these methods, the goal of the present work is to analyse which is the best way to select the controlled nodes, i.e. the one that guarantees the lower synchronization rate. We show that hubs are generally the most advantageous nodes to control, especially when the degree distribution is heterogeneous. Nevertheless, pinning a too large number of hubs is in general not an appropriate choice. Our results are in line with previous works that studied pinning control aimed to increase synchronization. These observations shed light on an interesting universality of good practice of node selection disregarding the actual goal of the control scheme.