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Multiscale dynamics in communities of phase oscillators
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10.1063/1.3672513
/content/aip/journal/chaos/22/1/10.1063/1.3672513
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/1/10.1063/1.3672513
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

An S = 0 equilibrium with five groups, and the corresponding equilateral pentagon. |ασ | = r 0 < 1 and σ = 1, 2, 3, 4, and 5.

Image of FIG. 2.
FIG. 2.

An equilibrium with S ≠ 0. The group order parameters lie on a straight line through the origin, and their magnitudes are all solutions to Eq. (17) .

Image of FIG. 3.
FIG. 3.

(Color) A sampling of oscillator phases from a numerical simulation with M = 3. Individual oscillator phases appear as solid dots on the unit circle, and the colors (red, green, and blue) correspond to different oscillator groups. Group order parameters ασ appear as larger open circles.

Image of FIG. 4.
FIG. 4.

(Color) Results for a case with three groups (M = 3), obtained by integrating Eq. (7) with , and defined as in Sec. IV A and the perturbations ωσ , δσ , and given by Eq. (63) . (a) The initial conditions, α 1(0) (red dot), α 2(0) (green dot), and α 3(0) (blue dot); (b) the evolution of |S|; (c) evolution of rσ with respect to r 0; (d) evolution of ψ 1, ψ 2, and ψ 3 (in radians); (e) evolution of , where . In (e), the horizontal line denotes the value w = wω  + wk given in Eq. (57) .

Image of FIG. 5.
FIG. 5.

(Color) Numerical results for three cases with four groups (M = 4). ((a), (c), and (e)) The evolution of ψ 1, ψ 2, ψ 3, and ψ 4 (in radians); ((b), (d), and (f)) the corresponding evolution of T. The pair switches in each simulation are possible only when the value of T nears zero. In (a) and (b), this occurs at t ≈ 130 and t ≈ 860. In (c) and (d), the pairs switch in a periodic manner throughout the simulation. In (e) and (f), we see that T ≈ 0 several times in the simulation but only one pair switch occurs, at t ≈ 35.

Image of FIG. 6.
FIG. 6.

(Color) Numerical results for a case with five groups (M = 5). (a) The evolution of ψ 1, ψ 2, ψ 3, ψ 4, and ψ 5 (in radians) and (b) the corresponding evolution of T. The value of T remains large throughout the simulation, in contrast to the cases with M = 4 in Fig. 5 .

Image of FIG. 7.
FIG. 7.

(Color) Numerical results for a case with six groups (M = 6). (a) The evolution of ψ 1, ψ 2, ψ 3, ψ 4, ψ 5, and ψ 6 (in radians) and (b) the corresponding evolution of T.

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/content/aip/journal/chaos/22/1/10.1063/1.3672513
2012-01-03
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multiscale dynamics in communities of phase oscillators
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/1/10.1063/1.3672513
10.1063/1.3672513
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