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Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator
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10.1063/1.4766678
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Affiliations:
1 Fundamental Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, Box 24 157 Douala, Cameroon and Salerno unit of CNSIM, Department of Physics, University of Salerno, I-84081 Fisciano, Italy
2 Department of Sciences for Biological, Geological, and Environmental Studies and Salerno unit of CNSIM, University of Sannio, Via Port'Arsa 11, I-82100 Benevento, Italy
3 Applied Mathematics Laboratory, University of Le Havre, 25 rue ph. Lebon, B.P 540, Le Havre, Cedex, France
4 Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271, Bloco II—Barra Funda, 01140-070 São Paulo, Brazil
a) Author to whom correspondence should be addressed. Electronic mail: ryamapi@yahoo.fr.
Chaos 22, 043114 (2012)
/content/aip/journal/chaos/22/4/10.1063/1.4766678
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4766678
View: Figures

## Figures

FIG. 1.

Parameters domain for the existence of a single limit cycle (white area) and three limit cycles (black area) solutions of Eq. for μ = 0.1.

FIG. 2.

Effect of the noise intensity D on the boundary between the region of one and three limit-cycle solutions in the parametric (α,β)-plane of the Fokker-Planck Eq. ) for μ = 0.1 as in Fig. .

FIG. 3.

Behavior of the residence times in the parameter space. The solid line denotes the locus , while circles and crosses denote the situation where and , respectively. The dashed line is the border of existence of birhythmicity. The noise level is D = 0.1.

FIG. 4.

Residence times as a function of the parameter α for different values of the parameter β. The noise level is D = 0.1, the nonlinearity μ = 0.1.

FIG. 5.

Residence times as a function of the parameter β for different values of the parameter α. The noise level is D = 0.1, the nonlinearity μ = 0.1.

FIG. 6.

Residence times as a function of the noise intensity D for different values of the parameter α. The second dissipation parameter reads β = 0.0005, the nonlinearity μ = 0.1.

FIG. 7.

Asymmetric probability distributions for different values of the noise intensity D versus the amplitude A when the frequencies of both attractors are identical, i.e., . Parameters of the system are μ = 0.1 and α = 0.083, β = 0.0014.

FIG. 8.

Probability distribution versus the amplitude A when the frequencies of the attractors are not identical i.e . Parameters of the system are D = 0.1, μ = 0.1, (i): α = 0.09, β = 0.0012, and (ii): α = 0.1, β = 0.014, .

FIG. 9.

Variation of the amplitudes and the bandwidths versus the noise intensity D. Lines and symbols denote analytical and numerical results, respectively. The circles and dot-dashed lines refer to the inner attractor , solid lines and triangles to the outer attractor . The parameters used are μ = 0.1, α = 0.1, β = 0.002.

FIG. 10.

Variation of the amplitudes and the bandwidths versus the noise intensity D. Lines and symbols denote analytical and numerical results, respectively. The circles and dot-dashed lines refer to the inner attractor , solid lines and triangles to the outer attractor . The parameters used are μ = 0.1, α = 0.12, β = 0.003.

FIG. 11.

Behavior of energy barriers versus α. Solid lines denote the analytical results, while dashed lines with triangles denote numerical simulations. Parameters of the system are μ = 0.1 and β = 0.002.

FIG. 12.

Behavior of energy barriers versus β. Solid lines denote the analytical results, while dashed lines with triangles denote numerical simulations. Parameters of the system are μ = 0.1 and α = 0.13.

/content/aip/journal/chaos/22/4/10.1063/1.4766678
2012-11-26
2014-04-21

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