69 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.
Exponential localization of singular vectors in spatiotemporal chaos
In a dynamical system the singular vector (SV) indicates which perturbation
will exhibit maximal growth after a time interval . We show that in
systems with spatiotemporal chaos the SV exponentially localizes in space.
Under a suitable transformation, the SV can be described in terms of the
Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us
to deduce a universal power law for the localization of the
SV. Moreover the same exponent characterizes the finite-
deviation of the Lyapunov exponent in excellent agreement with simulations. Our
results may help improving existing forecasting techniques.Comment: 5 page
Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
The emergence of collective synchrony from an incoherent state is a
phenomenon essentially described by the Kuramoto model. This canonical model
was derived perturbatively, by applying phase reduction to an ensemble of
heterogeneous, globally coupled Stuart-Landau oscillators. This derivation
neglects nonlinearities in the coupling constant. We show here that a
comprehensive analysis requires extending the Kuramoto model up to quadratic
order. This "enlarged Kuramoto model" comprises three-body (nonpairwise)
interactions, which induce strikingly complex phenomenology at certain
parameter values. As the coupling is increased, a secondary instability renders
the synchronized state unstable, and subsequent bifurcations lead to collective
chaos. An efficient numerical study of the thermodynamic limit, valid for
Gaussian heterogeneity, is carried out by means of a Fourier-Hermite
decomposition of the oscillator density.Comment: 6 pages, 3 figure
Volcano transition in populations of phase oscillators with random nonreciprocal interactions
Populations of heterogeneous phase oscillators with frustrated random
interactions exhibit a quasi-glassy state in which the distribution of local
fields is volcano-shaped. In a recent work [Phys. Rev. Lett. 120, 264102
(2018)] the volcano transition was replicated in a solvable model using a
low-rank, random coupling matrix . We extend here that model
including tunable nonreciprocal interactions, i.e. . More specifically, we formulate two different solvable models. In both of
them the volcano transition persists if matrix elements and
are enough correlated. Our numerical simulations fully confirm the analytical
results. To put our work in a wider context, we also investigate numerically
the volcano transition in the analogous model with a full-rank random coupling
matrix.Comment: To be published in Physical Review E. 9 pages, 7 figure
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
Logarithmic bred vectors in spatiotemporal chaos: structure and growth
Bred vectors are a type of finite perturbation used in prediction studies of
atmospheric models that exhibit spatially extended chaos. We study the
structure, spatial correlations, and the growth- rates of logarithmic bred
vectors (which are constructed by using a given norm). We find that, after a
suitable transformation, logarithmic bred vectors are roughly piecewise copies
of the leading Lyapunov vector. This fact allows us to deduce a scaling law for
the bred vector growth rate as a function of their amplitude. In addition, we
relate growth rates with the spectrum of Lyapunov exponents corresponding to
the most expanding directions. We illustrate our results with simulations of
the Lorenz '96 model.Comment: 8 pages, 8 figure
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
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