Jury
Prof. Joseph WINKIN (UNamur), Chair
Prof. Timoteo CARLETTI (UNamur), Secretary
Prof. Alexandre MAUROY (UNamur)
Prof. Malbor ASLLANI (Florida State University)
Dr. Maxime LUCAS (UNamur)
Dr. Riccardo MUOLO (RIKEN Institute)
Abstract
Synchronization is a ubiquitous phenomenon in the world around us. It is a crucial feature that ensures the proper functioning of many complex systems. The various generators in a power grid must produce alternating current at a common frequency, and the brain’s cortical regions synchronize their activities to enable the brain to control the human body. These systems can be modeled as coupled oscillators, as in the famous Kuramoto model, where entities interact in pairs so that they synchronize globally.
However, synchronization can also pose a problem. For instance, excessive synchronization of brain dynamics leads to pathological states such as epileptic seizures. It is therefore necessary to develop methods that reduce global synchronization by locally controlling the dynamics of certain oscillators. In particular, a control scheme based on a Hamiltonian framework has been designed to effectively desynchronize the Kuramoto model.
Nevertheless, some limitations remain. First, the controlled nodes are selected at random without considering their specific characteristics. Second, this method is designed to control systems with a network structure—that is, with pairwise coupling—whereas many recent studies have demonstrated the importance of higher-order networks, i.e., group interactions, in modeling such systems.
In this Ph.D. thesis, we aim to address these gaps through several studies. We explore the optimal method for selecting controlled nodes to maximize control efficiency, investigate the method’s ability to desynchronize systems with higher-order interactions, and develop a new control method tailored to this framework.
Our results not only improve these control techniques but also offer novel perspectives on the synchronization of complex systems. They allow us to better understand the influence of each local entity on collective behavior and the role played by interactions of different orders. Among other things, they shed light on the non-monotonic relationship between synchronization capacity and the strength of higher-order interactions.
