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

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

Authors :
Sekikawa, Munehisa
Inaba, Naohiko
Yoshinaga, Tetsuya
Hikihara, Takashi
Source :
Physics Letters A. Aug2010, Vol. 374 Issue 36, p3745-3751. 7p.
Publication Year :
2010

Abstract

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
03759601
Volume :
374
Issue :
36
Database :
Academic Search Index
Journal :
Physics Letters A
Publication Type :
Academic Journal
Accession number :
52874867
Full Text :
https://doi.org/10.1016/j.physleta.2010.07.033