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Kundan Lal DAS Munehisa SEKIKAWA Tadashi TSUBONE Naohiko INABA Hideaki OKAZAKI
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.
Tri Quoc TRUONG Tadashi TSUBONE Kuniyasu SHIMIZU Naohiko INABA
This report presents experimental measurements of mixed-mode oscillations (MMOs) generated by a weakly driven four-segment piecewise linear Bonhoeffer-van der Pol (BVP) oscillator. Such a roughly approximated simple piecewise linear circuit can generate MMOs and mixed-mode oscillation-incrementing bifurcations (MMOIBs). The laboratory experiments well agree with numerical results. We experimentally and numerically observe time series and Lorenz plots of MMOs generated by successive and nonsuccessive MMOIBs.