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Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator
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10.1063/1.4766678
/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

Image of FIG. 1.
FIG. 1.

Parameters domain for the existence of a single limit cycle (white area) and three limit cycles (black area) solutions of Eq. (1) for μ = 0.1.

Image of FIG. 2.
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. (11) ) for μ = 0.1 as in Fig. 1 .

Image of FIG. 3.
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.

Image of FIG. 4.
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.

Image of FIG. 5.
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.

Image of FIG. 6.
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.

Image of FIG. 7.
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.

Image of FIG. 8.
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, .

Image of FIG. 9.
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.

Image of FIG. 10.
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.

Image of FIG. 11.
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.

Image of FIG. 12.
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.

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/content/aip/journal/chaos/22/4/10.1063/1.4766678
2012-11-26
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4766678
10.1063/1.4766678
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