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Long-term fluctuations in globally coupled phase oscillators with general coupling: Finite size effects
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10.1063/1.3692966
/content/aip/journal/chaos/22/1/10.1063/1.3692966
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/1/10.1063/1.3692966
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Schematic view of D and V in the limit when the synchronization transition at is similar to the second order phase transition.

Image of FIG. 2.
FIG. 2.

(Color online) The time evolutions of the variance of the integrated order parameter (upper) and the correlation function C(t) (lower) in the Kuramoto model where and N = 24 000. (a) and (c) The coherent regime where . (b) and (d) The incoherent regime where . In both regimes, increases linearly with slope 2Dt after a transient period. The correlation function C(t) in the coherent regime has a characteristic time period in which , whereas the form of C(t) in the incoherent regime is almost exponential. Each plot is an average over 30 samples.

Image of FIG. 3.
FIG. 3.

(Color online) The scaling property of the diffusion coefficient D with system size N in the coherent regime of the Kuramoto model, where , and . Line fitting yields . Each plot is an average over 90 samples.

Image of FIG. 4.
FIG. 4.

(Color online) The diffusion coefficient D with an increase of system size N in the incoherent regime of the Kuramoto model, where . D fluctuates around a finite value for sufficiently large N. Each plot is an average over 90 samples.

Image of FIG. 5.
FIG. 5.

(Color online) The correlation function C(t) for N = 64 000 (a), the variance V (b), and the correlation time (c) of the order parameter in the incoherent regime of the Kuramoto model, where . C(t) almost exponentially decreases with t. V and fluctuate around a finite value for sufficiently large N. Each plot is an average over 90 samples.

Image of FIG. 6.
FIG. 6.

(Color online) The scaling property of the diffusion coefficient D with system size N (upper) and the correlation function C(t) (lower) in the coherent regime of system (1) with (a) and (d) and , (b) and (e) and , and (c) and (f) and , respectively, where for (a)-(c) and N = 24 000 for (d)-(f). Each plot is an average over 90 samples.

Image of FIG. 7.
FIG. 7.

(Color online) The diffusion coefficient D with an increase of system size N in the incoherent regime of system (1) with (a) and , (b) and , and (c) and . D fluctuates around a finite value for sufficiently large N. Each plot is an average over 90 samples.

Image of FIG. 8.
FIG. 8.

(Color online) The correlation function C(t) for N = 64 000 (left), the variance V (middle), and the correlation time (right) of the order parameter in the incoherent regime of system (1) with (a)–(c) and , (d)–(f) and , and (g)–(i) and . C(t) almost exponentially decreases with t. V and fluctuate around a finite value for sufficiently large N. Each plot is an average over 90 samples.

Image of FIG. 9.
FIG. 9.

(Color online) Schematic view of . (a) An incoherent state. (b) A coherent state.

Image of FIG. 10.
FIG. 10.

(Color online) The scaling property of the diffusion coefficient D with system size N in the coherent regime of the Kuramoto model, where , , and is deterministically generated. The line fitting yields . Each plot is an average over 10 different initial conditions.

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2012-03-21
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Long-term fluctuations in globally coupled phase oscillators with general coupling: Finite size effects
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/1/10.1063/1.3692966
10.1063/1.3692966
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