Boundary effects in extended dynamical systems

In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary conditions. For a nonlinear reaction-diffusion model we obtain boundary-induced spatially chaotic configurations. Nontrivial average patterns arising from boundaries are shown to appear in spatiotemporally chaotic states of the Kuramoto-Sivashinsky model. Finally, walls organize novel states in simulations of the complex Ginzburg-Landau equation.Comment: Proceedigs of LAWNP'99. To be published in Physica A. Uses the Elsart style. This short paper is intended as a summary of our recent work on boundary influences in extended dynamical systems, with links to more detailed papers. Related material at http://www.imedea.uib.es/PhysDept

Filament bifurcations in a one-dimensional model of reacting excitable fluid flow

Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the filament-like structures observed in the system. Here, we perform a bifurcation analysis of this one-dimensional approximation as a function of the {\it Damk{\"o}hler} number, the ratio between the chemical and the strain rates. Different branches of stable solutions are calculated, and a Hopf bifurcation, leading to an oscillating filament, identified.Comment: 9 pages, 4 figures; elsart.cls styl

Dynamics of Defects in the Vector Complex Ginzburg-Landau Equation

Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special symmetries and can be written as a vector complex Ginzburg-Landau equation. Dynamical properties of localized structures of topological character in this vector-field case are considered. Creation and annihilation processes of different kinds of vector defects are described, and some of them interpreted in theoretical terms. A transition between different regimes of spatiotemporal dynamics is described.Comment: 35 pages of LATeX, using the elsart macros. Includes 17 (large) figures. Related material, including movies and higher resolution figures, available at http://www.imedea.uib.es/PhysDept/Nonlinear/research_topics/Vcgl2

Localized structures in coupled Ginzburg-Landau equations

Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to a Hopf bifurcation leading to nonlinear oscillations. We study numerically this set of equations and find, within a particular range of parameters, the presence of uniformly propagating localized objects behaving as coherent structures. Some of these localized objects are interpreted in terms of exact analytical solutions.Comment: 7 pages, 3 postscript figures, uses the elsart style files. Related material availeble from http://www.imedea.uib.es/Nonlinea

Noise-induced flow in quasigeostrophic turbulence with bottom friction

Randomly-forced fluid flow in the presence of scale-unselective dissipation develops mean currents following topographic contours. Known mechanisms based on the scale-selective action of damping processes are not at work in this situation. Coarse-graining reveals that the phenomenon is a kind of noise-rectification mechanism, in which lack of detailed balance and the symmetry-breaking provided by topography play an important role.Comment: 8 pages Revtex, no figures. Related material at http://www.imedea.uib.es

Anticipating the dynamics of chaotic maps

We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.Comment: Uses the elsart.cls (v2000) style (included). 9 pages, including 4 figures. New version contains minor modifications to text and figure

Low-dimensional dynamical system model for observed coherent structures in ocean satellite data

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one obtained from the experimental data. We apply the procedure to analyze coherent structures in an oceanic setting, the ones arising from instabilities of the Algerian current, in the western Mediterranean Sea. Data are from satellite altimetry providing Sea Surface Height, and the model is a two-layer quasigeostrophic system. A four-dimensional dynamical system is obtained that correctly describe the observed coherent structures (moving eddies). Finally, a bifurcation analysis is performed on the reduced model.Comment: 23 pages, 7 figure