Synchronization of weakly coupled canard oscillators

Abstract : Synchronization has been studied extensively in the context of weakly coupled oscillators using the so-called phase response curve (PRC) which measures how a change of the phase of an oscillator is affected by a small perturbation. This approach was based upon the work of Malkin, and it has been extended to relaxation oscillators. Namely, synchronization conditions were established under the weak coupling assumption, leading to a criterion for the existence of synchronous solutions of weakly coupled relaxation oscillators. Previous analysis relies on the fact that the slow nullcline does not intersect the fast nullcline near one of its fold points, where canard solutions can arise. In the present study we use numerical continuation techniques to solve the adjoint equations and we show that synchronization properties of canard cycles are different than those of classical relaxation cycles. In particular, we highlight a new special role of the maximal canard in separating two distinct synchronization regimes: the Hopf regime and the relaxation regime. Phase plane analysis of slow–fast oscillators undergoing a canard explosion provides an explanation for this change of synchronization properties across the maximal canard.
Type de document :
Article dans une revue
Liste complète des métadonnées

Littérature citée [73 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01558897
Contributeur : Mathieu Desroches <>
Soumis le : mardi 11 juillet 2017 - 10:40:08
Dernière modification le : lundi 27 août 2018 - 11:44:02
Document(s) archivé(s) le : mercredi 24 janvier 2018 - 21:31:50

Fichier

KDK_PhysicaD_accepted.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Elif Köksal Ersöz, Mathieu Desroches, Martin Krupa. Synchronization of weakly coupled canard oscillators. Physica D: Nonlinear Phenomena, Elsevier, 2017, 349, pp.46-61. 〈http://www.sciencedirect.com/science/article/pii/S0167278916304912〉. 〈10.1016/j.physd.2017.02.016〉. 〈hal-01558897〉

Partager

Métriques

Consultations de la notice

225

Téléchargements de fichiers

104