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Phase and amplitude dynamics in large systems of coupled oscillators: Growth heterogeneity, nonlinear frequency shifts, and cluster states
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10.1063/1.4816361
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Affiliations:
1 Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
Chaos 23, 033116 (2013)
/content/aip/journal/chaos/23/3/10.1063/1.4816361
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4816361
View: Figures

## Figures

FIG. 1.

Schematics of .

FIG. 2.

The effect of dispersion in α ( ) with a Lorentzian . Stability/instability regions of space for several different values of spread in the linear growth parameter α with mean [Legend: black line ( ), red line ( ), and blue line ( )].

FIG. 3.

(a) Stability/instability regions of space for Lorentzian and several different values of the nonlinear frequency shift parameter [Legend: black line ( ), red line ( ), and blue line ( )]. Notice that the three lines coincide when . (b) For nonzero, the corresponding dependence of the critical frequency Ω at the transition from incoherence.

FIG. 4.

The effect of dispersion in α with a uniformly distributed , Eq. . Stability/instability regions of space for several different values of spread in the linear growth parameter α with mean [Legend: black line ( ), red line ( ), and blue line ( )].

FIG. 5.

(a) Stability/instability regions of space for a flat-top distribution and several different values of the nonlinear frequency shift parameter [Legend: black line ( ), red line ( ), and blue line ( )]. Notice that the three lines coincide when . (b) For nonzero, the corresponding dependence of the critical frequency Ω at the transition from incoherence.

FIG. 6.

Locations of 50 000 oscillators (black) in locked states with different . Twenty oscillators (red cross) of parameter values evenly spaced simultaneously in are highlighted, i.e., the oscillator with is located at the minimum radius position, and the oscillator with is located at the maximum radius position, and other oscillators of intermediate parameter values are distributed in between ( = 50 000, ; random initial conditions).

FIG. 7.

Time evolution of (top panel) and (bottom panel) for a system of 500 000 oscillators. (Parameters: ; random initial conditions.)

FIG. 8.

(a) Two-cluster locked state solutions. The blue line shows the curve for Eq. and the red line shows the curve for Eq. ; parameters: . (b) Blowup of the figure in (a) around (0, 0).

FIG. 9.

Simulation study of a two-cluster periodic state; parameters:  = 50 000, .

FIG. 10.

(a) Rotation number from numerical solutions versus the infinite rotation number for , and varied from 0.497 to 0.533 with . (b) and (c) Blowup of two regions of the figure in (a).

/content/aip/journal/chaos/23/3/10.1063/1.4816361
2013-07-24
2014-04-18

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