7,636 research outputs found

    Phase separation in coupled chaotic maps on fractal networks

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    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

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    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

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    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

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    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

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    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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