title: Using Hamiltonian control to desynchronize Kuramoto oscillators.
abstract: Many coordination phenomena are based on a synchronization process, whose global behavior emerges from the interactions among the individual parts. Often in nature, such self-organized mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are, however, cases where synchronization acts against the stability of the system; for instance in some neurodegenerative diseases or epilepsy or the famous case of Millennium Bridge where the crowd synchronization of the pedestrians seriously endangered the stability of the structure. In this paper we propose an innovative control method to tackle the synchronization process based on the application of the Hamiltonian control theory, by adding a small control term to the system we are able to impede the onset of the synchronization. We present our results on a generalized class of the paradigmatic Kuramoto model.
authors.affiliation: Department of Mathematics & Computer Science, University of Florence, Viale Morgagni 67/A, 50134 Florence, Italy.|naXys, Namur Center for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium.
authors.forename: Oltiana
authors.initials: O
authors.lastname: Gjata
authors.affiliation: naXys, Namur Center for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium.
authors.forename: Malbor
authors.initials: M
authors.lastname: Asllani
authors.affiliation: Department of Mathematics & Computer Science, University of Florence, Viale Morgagni 67/A, 50134 Florence, Italy.
authors.forename: Luigi
authors.initials: L
authors.lastname: Barletti
authors.affiliation: naXys, Namur Center for Complex Systems, University of Namur, rempart de la Vierge 8, B 5000 Namur, Belgium.
authors.forename: Timoteo
authors.initials: T
authors.lastname: Carletti