83 research outputs found
From quasiperiodic partial synchronization to collective chaos in populations of inhibitory neurons with delay
Collective chaos is shown to emerge, via a period-doubling cascade, from
quasiperiodic partial synchronization in a population of identical inhibitory
neurons with delayed global coupling. This system is thoroughly investigated by
means of an exact model of the macroscopic dynamics, valid in the thermodynamic
limit. The collective chaotic state is reproduced numerically with a finite
population, and persists in the presence of weak heterogeneities. Finally, the
relationship of the model's dynamics with fast neuronal oscillations is
discussed.Comment: 5 page
Collective synchronization in the presence of reactive coupling and shear diversity
We analyze the synchronization dynamics of a model obtained from the phase
reduction of the mean-field complex Ginzburg-Landau equation with
heterogeneity. We present exact results that uncover the role of dissipative
and reactive couplings on the synchronization transition when shears and
natural frequencies are independently distributed. As it occurs in the purely
dissipative case, an excess of shear diversity prevents the onset of
synchronization, but this does not hold true if coupling is purely reactive. In
this case the synchronization threshold turns out to depend on the mean of the
shear distribution, but not on all the other distribution's moments.Comment: To appear in Phys. Rev.
Time delay in the Kuramoto model with bimodal frequency distribution
We investigate the effects of a time-delayed all-to-all coupling scheme in a
large population of oscillators with natural frequencies following a bimodal
distribution. The regions of parameter space corresponding to synchronized and
incoherent solutions are obtained both numerically and analytically for
particular frequency distributions. In particular we find that bimodality
introduces a new time scale that results in a quasiperiodic disposition of the
regions of incoherence.Comment: 5 pages, 4 figure
Analysis of a power grid using the Kuramoto-like model
We show that there is a link between the Kuramoto paradigm and another system
of synchronized oscillators, namely an electrical power distribution grid of
generators and consumers. The purpose of this work is to show both the formal
analogy and some practical consequences. The mapping can be made quantitative,
and under some necessary approximations a class of Kuramoto-like models, those
with bimodal distribution of the frequencies, is most appropriate for the
power-grid. In fact in the power-grid there are two kinds of oscillators: the
'sources' delivering power to the 'consumers'.Comment: 24 pages, including 7 figures. To appear on Eur. Phys. J.
Time delay in the Kuramoto model with bimodal frequency distribution
5 pages.-- PACS numbers: 05.45.Xt, 89.75.Fb, 02.30.Ks.-- ArXiv pre-print: http://arxiv.org/abs/nlin.AO/0606045.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevE.74.056201.We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and incoherent solutions are obtained both numerically and analytically for particular frequency distributions. In particular, we find that bimodality introduces a new time scale that results in a quasiperiodic disposition of the regions of incoherence.E. M. was partially supported by the European research project EmCAP (FP6-IST, Contract No. 013123). J. S. was supported by Deutsche Forschungsgemeinschaft project SCH-1642/1-1
The Kuramoto model with distributed shear
We uncover a solvable generalization of the Kuramoto model in which shears
(or nonisochronicities) and natural frequencies are distributed and
statistically dependent. We show that the strength and sign of this dependence
greatly alter synchronization and yield qualitatively different phase diagrams.
The Ott-Antonsen ansatz allows us to obtain analytical results for a specific
family of joint distributions. We also derive, using linear stability analysis,
general formulae for the stability border of incoherence.Comment: 6 page
Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
We investigate the transition to synchronization in the Kuramoto model with
bimodal distributions of the natural frequencies. Previous studies have
concluded that the model exhibits a hysteretic phase transition if the bimodal
distribution is close to a unimodal one, due to the shallowness the central
dip. Here we show that proximity to the unimodal-bimodal border does not
necessarily imply hysteresis when the width, but not the depth, of the central
dip tends to zero. We draw this conclusion from a detailed study of the
Kuramoto model with a suitable family of bimodal distributions.Comment: 9 pages, 5 figures, to appear in Physical Review
Universal behavior in populations composed of excitable and self-oscillatory elements
We study the robustness of self-sustained oscillatory activity in a globally
coupled ensemble of excitable and oscillatory units. The critical balance to
achieve collective self-sustained oscillations is analytically established. We
also report a universal scaling function for the ensemble's mean frequency. Our
results extend the framework of the `Aging Transition' [Phys. Rev. Lett. 93,
104101 (2004)] including a broad class of dynamical systems potentially
relevant in biology.Comment: 4 pages; Changed titl
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