108 research outputs found
Transition to Stochastic Synchronization in Spatially Extended Systems
Spatially extended dynamical systems, namely coupled map lattices, driven by
additive spatio-temporal noise are shown to exhibit stochastic synchronization.
In analogy with low-dymensional systems, synchronization can be achieved only
if the maximum Lyapunov exponent becomes negative for sufficiently large noise
amplitude. Moreover, noise can suppress also the non-linear mechanism of
information propagation, that may be present in the spatially extended system.
A first example of phase transition is observed when both the linear and the
non-linear mechanisms of information production disappear at the same critical
value of the noise amplitude. The corresponding critical properties can be
hardly identified numerically, but some general argument suggests that they
could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely,
when the non-linear mechanism prevails on the linear one, another type of phase
transition to stochastic synchronization occurs. This one is shown to belong to
the universality class of directed percolation.Comment: 21 pages, Latex - 14 EPS Figs - To appear on Physical Review
Synchronization in coupled map lattices as an interface depinning
We study an SOS model whose dynamics is inspired by recent studies of the
synchronization transition in coupled map lattices (CML). The synchronization
of CML is thus related with a depinning of interface from a binding wall.
Critical behaviour of our SOS model depends on a specific form of binding
(i.e., transition rates of the dynamics). For an exponentially decaying binding
the depinning belongs to the directed percolation universality class. Other
types of depinning, including the one with a line of critical points, are
observed for a power-law binding.Comment: 4 pages, Phys.Rev.E (in press
Re-localization due to finite response times in a nonlinear Anderson chain
We study a disordered nonlinear Schr\"odinger equation with an additional
relaxation process having a finite response time . Without the relaxation
term, , this model has been widely studied in the past and numerical
simulations showed subdiffusive spreading of initially localized excitations.
However, recently Caetano et al.\ (EPJ. B \textbf{80}, 2011) found that by
introducing a response time , spreading is suppressed and any
initially localized excitation will remain localized. Here, we explain the lack
of subdiffusive spreading for by numerically analyzing the energy
evolution. We find that in the presence of a relaxation process the energy
drifts towards the band edge, which enforces the population of fewer and fewer
localized modes and hence leads to re-localization. The explanation presented
here is based on previous findings by the authors et al.\ (PRE \textbf{80},
2009) on the energy dependence of thermalized states.Comment: 3 pages, 4 figure
Collective motions in globally coupled tent maps with stochastic updating
We study a generalization of globally coupled maps, where the elements are
updated with probability . When is below a threshold , the
collective motion vanishes and the system is the stationary state in the large
size limit. We present the linear stability analysis.Comment: 6 pages including 5 figure
Infinities of stable periodic orbits in systems of coupled oscillators
We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor
A mechanical model of normal and anomalous diffusion
The overdamped dynamics of a charged particle driven by an uniform electric
field through a random sequence of scatterers in one dimension is investigated.
Analytic expressions of the mean velocity and of the velocity power spectrum
are presented. These show that above a threshold value of the field normal
diffusion is superimposed to ballistic motion. The diffusion constant can be
given explicitly. At the threshold field the transition between conduction and
localization is accompanied by an anomalous diffusion. Our results exemplify
that, even in the absence of time-dependent stochastic forces, a purely
mechanical model equipped with a quenched disorder can exhibit normal as well
as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure
Condensation in Globally Coupled Populations of Chaotic Dynamical Systems
The condensation transition, leading to complete mutual synchronization in
large populations of globally coupled chaotic Roessler oscillators, is
investigated. Statistical properties of this transition and the cluster
structure of partially condensed states are analyzed.Comment: 11 pages, 4 figures, revte
Rapid convergence of time-averaged frequency in phase synchronized systems
Numerical and experimental evidence is presented to show that many phase
synchronized systems of non-identical chaotic oscillators, where the chaotic
state is reached through a period-doubling cascade, show rapid convergence of
the time-averaged frequency. The speed of convergence toward the natural
frequency scales as the inverse of the measurement period. The results also
suggest an explanation for why such chaotic oscillators can be phase
synchronized.Comment: 6 pages, 9 figure
Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
We introduce a definition of a "localization width" whose logarithm is given
by the entropy of the distribution of particle component amplitudes in the
Lyapunov vector. Different types of localization widths are observed, for
example, a minimum localization width where the components of only two
particles are dominant. We can distinguish a delocalization associated with a
random distribution of particle contributions, a delocalization associated with
a uniform distribution and a delocalization associated with a wave-like
structure in the Lyapunov vector. Using the localization width we show that in
quasi-one-dimensional systems of many hard disks there are two kinds of
dependence of the localization width on the Lyapunov exponent index for the
larger exponents: one is exponential, and the other is linear. Differences, due
to these kinds of localizations also appear in the shapes of the localized
peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the
spatial and momentum parts of the Lyapunov vectors. We show that the Krylov
relation for the largest Lyapunov exponent as a
function of the density is satisfied (apart from a factor) in the same
density region as the linear dependence of the localization widths is observed.
It is also shown that there are asymmetries in the spatial and momentum parts
of the Lyapunov vectors, as well as in their and -components.Comment: 41 pages, 21 figures, Manuscript including the figures of better
quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm
Classical and quantum decay of one dimensional finite wells with oscillating walls
To study the time decay laws (tdl) of quasibounded hamiltonian systems we
have considered two finite potential wells with oscillating walls filled by non
interacting particles. We show that the tdl can be qualitatively different for
different movement of the oscillating wall at classical level according to the
characteristic of trapped periodic orbits. However, the quantum dynamics do not
show such differences.Comment: RevTeX, 15 pages, 14 PostScript figures, submitted to Phys. Rev.
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