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 ca...