Synchronization of weakly coupled canard oscillators - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Physica D: Nonlinear Phenomena Year : 2017

Synchronization of weakly coupled canard oscillators


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.
Fichier principal
Vignette du fichier
KDK_PhysicaD_accepted.pdf (4.85 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01558897 , version 1 (11-07-2017)



Elif Köksal Ersöz, Mathieu Desroches, Martin Krupa. Synchronization of weakly coupled canard oscillators. Physica D: Nonlinear Phenomena, 2017, 349, pp.46-61. ⟨10.1016/j.physd.2017.02.016⟩. ⟨hal-01558897⟩
282 View
237 Download



Gmail Facebook X LinkedIn More