This paper discusses the synchronization of two identical canard-generating oscillators. First, we investigate a canard explosion generated in a system containing a Bonhoeffer-van der Pol (BVP) oscillator using the actual parameter values obtained experimentally. We find that it is possible to numerically observe a canard explosion using this dynamic oscillator. Second, we analyze the complete and in-phase synchronizations of identical canard-generating coupled oscillators via experimental and numerical methods. However, we experimentally determine that a small decrease in the coupling strength of the system induces the collapse of the complete synchronization and the occurrence of a complex synchronization; this finding could not be explained considering four-dimensional autonomous coupled BVP oscillators in our numerical work. To numerically investigate the experimental results, we construct a model containing coupled BVP oscillators that are subjected to two weak periodic perturbations having the same frequency. Further, we find that this model can efficiently numerically reproduce experimentally observed synchronization.

This study investigates quasiperiodic bifurcations generated in a coupled delayed logistic map. Since a delayed logistic map generates an invariant closed curve (ICC), a coupled delayed logistic map exhibits an invariant torus (IT). In a parameter region generating IT, ICC-generating regions extend in many directions like a web. This bifurcation structure is called an Arnol'd resonance web. In this study, we investigate the bifurcation structure of Chenciner bubbles, which are complete synchronization regions in the parameter space, and illustrate a complete bifurcation set for one of Chenciner bubbles. The bifurcation boundary of the Chenciner bubbles is surrounded by saddle-node bifurcation curves and Neimark-Sacker bifurcation curves.