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

Abstract Synchronization is an ubiquitous phenomenon in systems composed of coupled oscillators. While it is often beneficial to the system under consideration, there are nevertheless relevant examples where one would like to reduce it, e.g. in brain dynamics. Indeed although synchronization is essential to the good functioning of brain dynamics, hyper-synchronization can induce problems such as epilepsy seizures. Motivated by this problem, we study a pinning control scheme able to decrease synchronization in a system of coupled Kuramoto oscillators, by focusing on the determination of the best selection strategy for the controllers, i.e. capable to guarantee a lower synchronization level. We show that hubs are generally the most advantageous nodes to control, especially when the degree distribution is heterogeneous. Nevertheless in cases of homogeneous degree distribution having a large distance between pinned nodes, in term of network shortest path length, appears to be also a key factor. We challenge the analytical findings on both synthetic and empirical networks, e.g. brain connectome. Our results are in line with previous works that studied pinning control with the opposite goal, i.e. increasing synchronization. These observations shed light on an interesting universality of good practice of node selection disregarding the actual goal of the control scheme.