Journal
PHYSICS LETTERS A
Volume 374, Issue 36, Pages 3745-3751Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2010.07.033
Keywords
Andronov-Hopf bifurcations; Mixed-mode oscillations; Canards; Chaos
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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. (C) 2010 Elsevier B.V. All rights reserved.
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