dorsal/arxiv
View SchemaCollective synchronization in populations of globally coupled phase oscillators with drifting frequencies
| Authors | Jacques Rougemont, Felix Naef |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0509036 |
| URL | https://arxiv.org/abs/q-bio/0509036 |
| DOI | 10.1103/PhysRevE.73.011104 |
Abstract
We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show that the incoherent state is unstable passed a critical coupling strength $K_c(\ga, \sigf)$, where $\ga$ is the inverse characteristic drifting time and $\sigf$ the asymptotic frequency dispersion. Expectedly $K_c$ agrees with the noisy Kuramoto model in the large $\ga$ (Schmolukowski) limit but increases slower as $\ga$ decreases. Asymptotic expansion of the solution for $\ga\to 0$ shows that the noiseless Kuramoto model with Gaussian frequency distribution is recovered in that limit. Thus varying a single parameter allows to interpolate smoothly between two regimes: one dominated by the frequency dispersion and the other by phase diffusion.
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"abstract": "We generalize the Kuramoto model for coupled phase oscillators by allowing\nthe frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such\ndrifting frequencies were recently measured in cellular populations of\ncircadian oscillator and inspired our work. Linear stability analysis of the\nFokker-Planck equation for an infinite population is amenable to exact solution\nand we show that the incoherent state is unstable passed a critical coupling\nstrength $K_c(\\ga, \\sigf)$, where $\\ga$ is the inverse characteristic drifting\ntime and $\\sigf$ the asymptotic frequency dispersion. Expectedly $K_c$ agrees\nwith the noisy Kuramoto model in the large $\\ga$ (Schmolukowski) limit but\nincreases slower as $\\ga$ decreases. Asymptotic expansion of the solution for\n$\\ga\\to 0$ shows that the noiseless Kuramoto model with Gaussian frequency\ndistribution is recovered in that limit. Thus varying a single parameter allows\nto interpolate smoothly between two regimes: one dominated by the frequency\ndispersion and the other by phase diffusion.",
"arxiv_id": "q-bio/0509036",
"authors": [
"Jacques Rougemont",
"Felix Naef"
],
"categories": [
"q-bio.QM",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevE.73.011104",
"title": "Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies",
"url": "https://arxiv.org/abs/q-bio/0509036"
},
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