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Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation |
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| Authors: | Kuniyasu Shimizu Munehisa Sekikawa Naohiko Inaba |
| Institution: | a Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, Chiba 275-0016, Japan b Aihara Innovative Mathematical Modelling Project, FIRST, JST, Tokyo 153-8505, Japan c Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan d Department of Electronics and Bioinformatics, Meiji University, Kawasaki 214-8571, Japan |
| Abstract: | 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. |
| Keywords: | The driven Bonhoeffer-van der Pol oscillator Subcritical Andronov-Hopf bifurcation Mixed-mode oscillations Chaos |
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