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

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• 作者：Munehisa Sekikawa ; Naohiko Inaba ; Tetsuya Yoshinaga ; Takashi Hikihara
• 关键词：Andronov– ; Hopf bifurcations ; Mixed-mode oscillations ; Canards ; Chaos
• 刊名：Physics Letters A
• 出版年：2010
• 出版时间：9 August 2010
• 年：2010
• 卷：374
• 期：36
• 页码：3745-3751
• 全文大小：788 K

文摘

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.