7,636 research outputs found
Phase separation in coupled chaotic maps on fractal networks
The phase ordering dynamics of coupled chaotic maps on fractal networks are
investigated. The statistical properties of the systems are characterized by
means of the persistence probability of equivalent spin variables that define
the phases. The persistence saturates and phase domains freeze for all values
of the coupling parameter as a consequence of the fractal structure of the
networks, in contrast to the phase transition behavior previously observed in
regular Euclidean lattices. Several discontinuities and other features found in
the saturation persistence curve as a function of the coupling are explained in
terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE
Antiferromagnetic effects in Chaotic Map lattices with a conservation law
Some results about phase separation in coupled map lattices satisfying a
conservation law are presented. It is shown that this constraint is the origin
of interesting antiferromagnetic effective couplings and allows transitions to
antiferromagnetic and superantiferromagnetic phases. Similarities and
differences between this models and statistical spin models are pointed out.Comment: 14 pages including 9 figure
On the Collective Motion in Globally Coupled Chaotic Systems
A mean-field formulation is used to investigate the bifurcation diagram for
globally coupled tent maps by means of an analytical approach. It is shown that
the period doubling sequence of the single site map induces a continuous family
of periodic states in the coupled system. This type of collective motion breaks
the ergodicity of the coupled map lattice. The stability analysis suggests that
these states are stable for weak coupling strength but opens the possibility
for more complicated types of motion in the regime of moderate coupling.Comment: 12 pages, Latex, 3 eps figures included also available "at
http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html" or "at
ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram/" Phys. Rep.
in pres
Phase growth in bistable systems with impurities
A system of coupled chaotic bistable maps on a lattice with randomly
distributed impurities is investigated as a model for studying the phenomenon
of phase growth in nonuniform media. The statistical properties of the system
are characterized by means of the average size of spatial domains of equivalent
spin variables that define the phases. It is found that the rate at which phase
domains grow becomes smaller when impurities are present and that the average
size of the resulting domains in the inhomogeneous state of the system
decreases when the density of impurities is increased. The phase diagram
showing regions where homogeneous, heterogeneous, and chessboard patterns occur
on the space of parameters of the system is obtained. A critical boundary that
separates the regime of slow growth of domains from the regime of fast growth
in the heterogeneous region of the phase diagram is calculated. The transition
between these two growth regimes is explained in terms of the stability
properties of the local phase configurations. Our results show that the
inclusion of spatial inhomogeneities can be used as a control mechanism for the
size and growth velocity of phase domains forming in spatiotemporal systems.Comment: 7 pages, 12 figure
Inherent global stabilization of unstable local behavior in coupled map lattices
The behavior of two-dimensional coupled map lattices is studied with respect
to the global stabilization of unstable local fixed points without external
control. It is numerically shown under which circumstances such inherent global
stabilization can be achieved for both synchronous and asynchronous updating.
Two necessary conditions for inherent global stabilization are derived
analytically.Comment: 17 pages, 10 figures, accepted for publication in Int.J.Bif.Chao
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