Certification of almost global phase synchronization of all-to-all coupled phase oscillators - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Chaos, Solitons & Fractals Année : 2023

Certification of almost global phase synchronization of all-to-all coupled phase oscillators

Résumé

Coupled oscillators may exhibit almost global phase synchronization, namely their phases tend to asymptotically overlap for almost all initial conditions. We consider certification of this property using Rantzer's dual Lyapunov approach with sum of squares (SOS) programming. To this aim, we use a stereographic transformation from a hypertorus to an Euclidean space. For the case of all-to-all coupling, this transformation converts the problem of certifying stability into the problem of certifying divergence of almost all solutions to infinity. We show that the latter can be solved using a polynomial Lyapunov density, which can be constructed via SOS programming. This leads to the certification of almost global phase synchronization of all-to-all coupled phase oscillators. We apply our method to an example of coupled phase oscillators and to an example of coupled van der Pol oscillators, and show that it can support the existing tools of local stability analysis by ensuring almost global phase synchronization. © 2023 Elsevier Ltd
Fichier non déposé

Dates et versions

hal-04194981 , version 1 (04-09-2023)

Identifiants

Citer

Mahmut Kudeyt, Ayşegül Kıvılcım, Elif Köksal-Ersöz, Ferruh İlhan, Özkan Karabacak. Certification of almost global phase synchronization of all-to-all coupled phase oscillators. Chaos, Solitons & Fractals, 2023, 174, pp.113838. ⟨10.1016/j.chaos.2023.113838⟩. ⟨hal-04194981⟩
4 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More