Spectral properties and pattern selection in fractal growth networks

A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at the nodes of a fractal growth network is given by a nonlinear map, giving raise to a coupled map system. The coupling is described by a matrix whose eigenvectors constitute a basis on which spatial patterns on fractal growth networks can be expressed by linear combination. The spectrum of eigenvalues the coupling matrix exhibits a nonuniform distribution that is reflected in the presence of gaps or niches in the boundaries of stability of the synchronized states on the space of parameters of the system. These gaps allow for the selection of specific spatial patterns by appropriately varying the parameters of the system.Comment: 9 pages, 6 Figs, Submitted to Physica

Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern.Comment: 3 pages, 3 figures, Accepted in European Physics Journa

Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given time. It is shown that the reinjection of the mean field to a fraction of randomly selected elements can induce synchronization and nontrivial collective behavior in the system. The regions where these collective states emerge on the space of parameters of the system are calculated.Comment: 2 pages, 2 figs, accepted in The European Physical Journa

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

Synchronization in driven versus autonomous coupled chaotic maps

The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction. It is shown that chaotic synchronized states in both systems are equivalent, but the collective states arising after the chaotic synchronized state becomes unstable can be different in these two systems. It is found that the external drive induces chaotic synchronization as well as synchronization of unstable periodic orbits of the local dynamics in the driven lattice. On the other hand, the addition of a global interaction in the autonomous system allows for chaotic synchronization that is not possible in a large coupled map system possessing only local couplings.Comment: 4 pages, 3 figs, accepted in Phys. Rev.