Period-doubling cascades of canards from the extended Bonhoeffer–van der Pol oscillator

• DOI: 10.1016/j.physleta.2010.07.033
• Publication Date: 2010-07-17T04:49:54Z
• Authors: Munehisa Sekikawa; Naohiko Inaba; Tetsuya Yoshinaga; Takashi Hikihara
• Keywords: Mixed-mode oscillations; Canards; Andronov–Hopf bifurcations; Chaos; Andronov-Hopf bifurcations

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.