Synchronization of canards in resistively and capacitively coupled canard-generating Bonhoeffer-van der Pol oscillators

Abstract

This letter presents an investigation into the synchronization of an autonomous system comprising two nearly identical canard-generating Bonhoeffer-van der Pol (BVP) oscillators coupled via a resistor and a capacitor in parallel. We first demonstrate via numerical simulations that this system exhibits butterfly synchronization, i.e., a phase shift between the canards in a weakly coupled system of nearly identical canard-generating BVP oscillators. Furthermore, the butterfly synchronization in the coupled system is observed experimentally.