Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation

In this study, we propose a remarkably simple oscillator that exhibits extremely complicated behaviors. The second-order nonautonomous differential equation discussed in this Letter is considered to be one of the simplest dynamics that can produce mixed-mode oscillations (MMOs) and chaos. Our model...

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Bibliographic Details
Published in:Physics letters. A 2011-04, Vol.375 (14), p.1566-1569
Main Authors: Shimizu, Kuniyasu, Sekikawa, Munehisa, Inaba, Naohiko
Format: Article
Language:English
Subjects:
Boundary value problems
Chaos
Chaos theory
Mathematical analysis
Mathematical models
Mixed-mode oscillations
Oscillations
Oscillators
Perturbation methods
Solid state physics
Subcritical Andronov–Hopf bifurcation
The driven Bonhoeffer–van der Pol oscillator
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Summary:In this study, we propose a remarkably simple oscillator that exhibits extremely complicated behaviors. The second-order nonautonomous differential equation discussed in this Letter is considered to be one of the simplest dynamics that can produce mixed-mode oscillations (MMOs) and chaos. Our model uses a Bonhoeffer–van der Pol (BVP) oscillator under weak periodic perturbation. The parameter set of the BVP equation is chosen such that a focus and a relaxation oscillation coexist when no perturbation is applied. Under weak periodic perturbation, various types of MMOs and chaos with remarkably complicated waveforms are observed. ► We propose a remarkably simple oscillator exhibiting extremely complicated behaviors. ► The oscillator can produce mixed-mode oscillations (MMOs) and chaos. ► Our model uses a BVP oscillator under weak periodic perturbation. ► The parameter set is chosen so that two solutions coexist without perturbation. ► Under weak periodic perturbation, various types of MMOs and chaos are observed.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.02.053