8 research outputs found
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