Synchronization of weakly coupled canard oscillators
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Date
2017-03-22
Authors
Köksal Ersöz, Elif
Desroches, Mathieu
Krupa, Martin
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier B.V.
Published Version
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.
Description
Keywords
Canards , Phase response curves , Slow–fast systems , Synchronization , Weak coupling
Citation
Köksal Ersöz, E., Desroches, M. and Krupa, M. (2017) 'Synchronization of weakly coupled canard oscillators', Physica D: Nonlinear Phenomena, 349, pp. 46-61, doi: 10.1016/j.physd.2017.02.016