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Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action
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10.1063/1.3247089
/content/aip/journal/chaos/19/4/10.1063/1.3247089
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/4/10.1063/1.3247089
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The qualitative trend of chaos observed in the first quadrant of the parameter plane is indicated by the shaded gradient. As the shade darkens near the bifurcation curve , chaos fills increasingly larger regions of the submanifolds containing the sinusoidal initial distributions. Points (A) and (B) are chosen as (1/20, 3/4) and (17/10, 1), respectively. Representative Poincaré sections for these points are shown in Figs. 2 and 3. The region is grayed out to represent that negative values of are not physical.

Image of FIG. 2.
FIG. 2.

Poincaré sections of at for a resistively loaded series array of Josephson junctions with [point (A) in Fig. 1]. The initial distributions are sinusoidal with wavenumber , where is (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, (i) 16, (j) 32, and (k) , i.e., on the Poisson submanifold. In (j) and (k), the complete trajectories are plotted instead of the intersections with the plane .

Image of FIG. 3.
FIG. 3.

Poincaré sections of at for a resistively loaded series array of Josephson junctions with [point (B) in Fig. 1]. The initial distributions are sinusoidal with wavenumber , where is (a) 1, (b) 2, (c) 4, (d) 8, (e) 16, (f) 32, (g) 64, and (h) , i.e., on the Poisson submanifold. In (g) and (h), the full trajectories are plotted.

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/content/aip/journal/chaos/19/4/10.1063/1.3247089
2009-10-15
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/4/10.1063/1.3247089
10.1063/1.3247089
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