Stochastic analog to phase transitions in chaotic coupled map lattices (original) (raw)
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Phase ordering in chaotic map lattices with conserved dynamics
Physical Review E, 1999
Dynamical scaling in a two-dimensional lattice model of chaotic maps, in contact with a thermal bath at temperature T , is numerically studied. The model here proposed is equivalent to a conserved Ising model with couplings which fluctuate over the same time scale as spin moves. When couplings fluctuations and thermal fluctuations are both important, this model does not belong to the class of universality of a Langevin equation known as model B; the scaling exponents are continuously varying with T and depend on the map used. The universal behavior of model B is recovered when thermal fluctuations are dominant.
Phase transitions in 2D linearly stable coupled map lattices
Physica D: Nonlinear Phenomena, 1997
Interlace dynamics separating homogeneous phases is shown to be the main mechanism underlying irregular evolution in 2D linearly stable, coupled map lattices. In a fully deterministic model belonging to this class, we find evidence of at least two different regimes that we call weak and strong turbulence. The transition between the two regimes is carefully investigated revealing a direct connection with the destabilization of the interfaces separating homogeneous phases. The critical behaviour i~ analysed and compared with that of stochastic models like directed percolation.
Collective behavior in coupled chaotic map lattices with random perturbations
Physica A: Statistical Mechanics and its Applications, 2008
Numerical simulations of coupled map lattices with non-local interactions (i.e., the coupling of a given map occurs with all lattice sites) often involve a large computer time if the lattice size is too large. In order to study dynamical effects which depend on the lattice size we considered the use of small truncated lattices with random inputs at their boundaries chosen from a uniform probability distribution. This emulates a "thermal bath", where deterministic degrees of freedom exhibiting chaotic behavior are replaced by random perturbations of finite amplitude. We demonstrate the usefulness of this idea to investigate the occurrence of completely synchronized chaotic states as the coupling parameters are varied. We considered one-dimensional lattices of chaotic logistic maps at outer crisis x → 4x(1 − x).
Ising-Type and Other Transitions in One-Dimensional Coupled Map Lattices with Sign Symmetry
2001
We consider a one-dimensional lattice of expanding antisymmetric maps [&1, 1] Ä [&1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter = is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as = grows beyond some critical value = c. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as = approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.
Antiferromagnetic effects in chaotic map lattices with a conservation law
Physics Letters A, 2003
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.
Spatiotemporal chaos in one- and two-dimensional coupled map lattices
Physica D: Nonlinear Phenomena, 1989
Coupled map lattices are investigated as a model for spatiotemporal chaos. Pattern dynamics in diffusivel~y coupled logistic lattice is briefly reviewed with the use of power spectra, domain distribution, a~d Lyapunov spectra. Mechanism of pattern selection with the suppression of chaos is discussed. Pattern dynamics on a 2-dimensional lattice is shown, in a weak coupling regime, a similarity with the one-dimensional case is found; frozen random pattern, pattern selection, Brownian motion of a chaotic string, and intermittent collapse of the pattern with selective flicker noise. In a strong coupling regime, frozen pattern is found to be unstable by the surface tension, which is in contrast with the one-dimensional case. Convective coupling model is introduced in connection with the fluid turbulence of Navier-Stokes type. Soliton turbulence and vortex turbulence in the model are reported. Physical implications of coupled map lattices are discussed.
Physica A: Statistical Mechanics and its Applications, 2006
Spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales, characterized by repeated conversions from spatially localized transient chaos into global laminar patterns. A simple model, yet retaining some features of more complex systems, consists of a lattice of a class of tent maps with an escaping region. The coupling prescription we adopt in this work considers the interaction of a site with all its neighbors, the corresponding strength decaying with the lattice distance as a power-law. This makes possible to pass continuously from a local (nearest-neighbor) to a global kind of coupling. We investigate statistical properties of both the chaotic transient bursts and the periodic laminar states, with respect to the coupling parameters.
Phase ordering in chaotic map lattices with additive noise
Physics Letters A, 2001
We present some result about phase separation in coupled map lattices with additive noise. We show that additive noise acts as an ordering agent in this class of systems. In particular, in the weak coupling region, a suitable quantity of noise leads to complete ordering. Extrapolating our results at small coupling, we deduce that this phenomenon could take place also in the limit of zero coupling.
Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that "solitons" can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but finite lifetimes, it is more reminiscent of a first-order transition. In the second-order regime, the deterministic model behaves like directed percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second- to first-order behavior ...