Soutenance publique de thèse de doctorat en Sciences mathématiques - Martin Moriamé

On the desynchronization of coupled Kuramoto oscillators

Jury

Prof. Joseph WINKIN (UNamur), Président
Prof. Timoteo CARLETTI (UNamur), Secrétaire
Prof. Alexandre MAUROY (UNamur)
Prof. Malbor ASLLANI (Florida State University)
Dr Maxime LUCAS (UNamur)
Dr Riccardo MUOLO (RIKEN Institute)

Résumé

Synchronization is a ubiquitous phenomenon in our surrounding world. It is a crucial feature guaranteeing the good functioning of many complex systems. The different generators in a power grid have to emit alternative current at a common rhythm, the brain cortical regions synchronize their activities to enable the brain to pilot the human body. Those systems can be modeled coupled oscillators, like in the famous Kuramoto model, where the entities interact by pairs so that they globally synchronize.

However, synchronization can also be an issue. For instance, a too strong synchronization of the brain dynamics leads to pathological states like epileptic seizures. It is thus needed to develop methods allowing to reduce the global synchronization by locally controlling the dynamics of some oscillators. In particular, a control scheme based on a Hamiltonian framework has been designed to effectively desynchronize the Kuramoto model.

Nevertheless, some limitations remain. Firstly, the controlled nodes are selected at random without considering their particular features. Secondly, this method is designed to control systems coupled with a network structure, i.e., with a pairwise coupling, whereas many recent works demonstrated the relevance of higher-order networks, i.e., group interactions, in the modeling of such systems.

In this PhD thesis, we aim to fill those gaps through several works. We explore the best way to select the controlled nodes so that the control is the most efficient, study its capacity to desynchronize systems with higher-order interactions and develop a new control method adapted to the latter framework.

Our results not only improve those 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 the collective behavior and the role played by the interactions of different orders. Among other things, they shed light on the non-monotonic relation between the synchronization capacity and the higher-order interaction strength.

 

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