https://doi.org/10.1140/epjb/e2017-80118-4
Regular Article
Coherence and stochastic resonance in a birhythmic van der Pol system
1 Fundamental Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, Box 24, 157 Douala, Cameroon
2 Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
3 Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, Box 812, Yaoundé, Cameroon
4 Dept. of Sciences and Technology and Salerno unit of CNSIM, University of Sannio, via Port’Arsa 11, 82100 Benevento, Italy
a
e-mail: ryamapi@yahoo.fr
Received: 25 February 2017
Received in final form: 19 May 2017
Published online: 9 August 2017
We consider the response to uncorrelated noise and harmonic excitation of a birhythmic van der Pol-type oscillator. This system, as opposed to the standard van der Pol oscillator, is characterized by two stable orbits. The noisy oscillator can be analytically mapped, with the technique of stochastic averaging, onto an ordinary bistable system with a bistable (quasi)potential. The birhythmic oscillator can also be numerically characterized through the diagnostics of coherent resonance and the signal-to-noise-ratio. The analysis shows the presence of noise-induced coherent states, influenced by the different time scales of the oscillator.
Key words: Statistical and Nonlinear Physics
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