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Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator |
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| Authors: | Munehisa Sekikawa Naohiko Inaba Takashi Hikihara |
| Institution: | a Department of Electrical Engineering, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo, Kyoto, 615-8510, Japan b Department of Electronics and Bioinformatics, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki, 214-8571, Japan c Institute of Health Biosciences, The University of Tokushima, 3-18-15 Kuramoto-cho, Tokushima, 770-8509, Japan |
| Abstract: | This Letter investigates the period-doubling cascades of canards, generated in the extended Bonhoeffer-van der Pol oscillator. Canards appear by Andronov-Hopf bifurcations (AHBs) and it is confirmed that these AHBs are always supercritical in our system. The cascades of period-doubling bifurcation are followed by mixed-mode oscillations. The detailed two-parameter bifurcation diagrams are derived, and it is clarified that the period-doubling bifurcations arise from a narrow parameter value range at which the original canard in the non-extended equation is observed. |
| Keywords: | Andronov-Hopf bifurcations Mixed-mode oscillations Canards Chaos |
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