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Canard-Mediated (De)Synchronization in Coupled Phantom Bursters

Abstract : In this work, we study canard-mediated transitions in mutually coupled phantom bursters. We extend a multiple-timescale model which provides a sequence of dynamic events, i.e., transition from a frequency modulated relaxation cycle to a quasi-steady-state and resumption of the relaxation regime through small amplitude oscillations. Folded singularities and associated canard solutions have a particular impact on the dynamics of the original system, which consists of two feedforward coupled FitzHugh--Nagumo oscillators, where the slow subsystem (regulator) controls the periodic behavior of the fast subsystem (secretor). We first investigate the variability in the dynamics depending on the canard mechanism that occurs near the folded singularities of the four-dimensional secretor-regulator configuration. Then, we introduce a second secretor and focus on the slow-fast transitions in the presence of a linear coupling between the secretors. In particular, we explore the impact of the relationship between the canard structures and the coupling on patterns of synchronization and desynchronization of the collective dynamics of the resulting six-dimensional system. We identify two different sources of desynchronization induced by canards, near a folded-saddle singularity and a folded-node singularity, respectively.
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Contributor : Frederique Clement <>
Submitted on : Thursday, January 14, 2016 - 5:03:09 PM
Last modification on : Thursday, January 7, 2021 - 3:26:09 PM




Elif Köksal Ersöz, Mathieu Desroches, Maciej Krupa, Frédérique Clément. Canard-Mediated (De)Synchronization in Coupled Phantom Bursters. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2016, 15 (1), pp.580-608. ⟨10.1137/15M101840X⟩. ⟨hal-01256389⟩



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