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

Minimal model for active nematics: quasi-long-range order and giant fluctuations

We propose a minimal microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like transition to quasi-long-range orientational order and that in this non-equilibrium context, the ordered phase is characterized by giant density fluctuations, in agreement with the predictions of Ramaswamy {\it et al.} [Europhys. Lett. {\bf 62}, 196 (2003)].Comment: Submitted to Phys. Rev. Lett. 4 pages, 4 figure

Spatiotemporal Chaos, Localized Structures and Synchronization in the Vector Complex Ginzburg-Landau Equation

We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg-Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist simultaneously in different regions of the space, and they are mediated by localized structures. A quantitative characterization of the degree of synchronization is given in terms of mutual information measures.Comment: 6 pages, using bifchaos.sty (included). 7 figures. Related material, including higher quality figures, could be found at http://www.imedea.uib.es/PhysDept/publicationsDB/date.html . To appear in International Journal of Bifurcation and Chaos (1999

Chaos induced coherence in two independent food chains

Coherence evolution of two food web models can be obtained under the stirring effect of chaotic advection. Each food web model sustains a three--level trophic system composed of interacting predators, consumers and vegetation. These populations compete for a common limiting resource in open flows with chaotic advection dynamics. Here we show that two species (the top--predators) of different colonies chaotically advected by a jet--like flow can synchronize their evolution even without migration interaction. The evolution is charaterized as a phase synchronization. The phase differences (determined through the Hilbert transform) of the variables representing those species show a coherent evolution.Comment: 5 pages, 5 eps figures. Accepted for publication in Phys. Rev.

Lyapunov Potential Description for Laser Dynamics

We describe the dynamical behavior of both class A and class B lasers in terms of a Lyapunov potential. For class A lasers we use the potential to analyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the steady state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the relaxation oscillations to the potential is found. We have included in this expression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semi-empirical relation giving the period of the relaxation oscillations far from the stationary state is proposed and checked against numerical simulations.Comment: 13 pages (including 7 figures) LaTeX file. To appear in Phys Rev.A (June 1999

Diffusion parameter control of spatiotemporal chaos

The stabilization of periodic solutions in the regime of spatiotemporal chaos through a diffusion parameter control is studied. We show that unstable plane waves in the Complex Ginzburg-Landau equation can be effectively stabilized in chaotic regimes such as phase turbulence and spatiotemporal intermittency or defect turbulence.Financial support from Direcci´on General de Investigaci ´on Cient´ıfica y T´ecnica (DGICYT, Spain), Projects PB94-1167 and PB94-1172, is acknowledged. R.M. also acknowledges partial support fromthe Programa de Desarrollo de Ciencias B´asicas (PEDECIBA, Uruguay).Peer Reviewe

Nonlinear diffusion control of spatiotemporal chaos in the complex Ginzburg-Landau equation

The role of nonlinear diffusion terms in the stability of periodic solutions in the regime of spatiotemporal chaos is studied. The stabilization of unstable plane waves in the complex Ginzburg-Landau equation in weakly chaotic regimes such as phase turbulence and spatiotemporal intermittency or in strong chaotic ones such as defect turbulence is demonstrated.Financial support from DGICYT Spain Project Nos. PB94-1167 and PB94-1172 is acknowledged. R.M. also acknowledges partial support from the Programa de Desarrollo de Ciencias Basicas PEDECIBA, Uruguay, the Consejo Nacional de Investigaciones Cientıficas y Tecnicas CONICYT, Uruguay, and the Programa de Cooperacion con Iberoamerica ICI, SpainPeer Reviewe

On some localized solutions of coupled Ginzburg-Landau equations

7 pages, 3 figures.-- Book TOC available at Google Books: http://books.google.es/books?isbn=1402018258The contents of this book correspond to Sessions VII and VIII of the International Workshop on Instabilities and Nonequilibrium Structures which took place in Viña del Mar, Chile, in December 1997 and December 1999, respectively. Part I is devoted to self-contained courses. Three courses are related to new developments in Bose-Einstein condensation: the first one by Robert Graham studies the classical dynamics of excitations of Bose condensates in anisotropic traps, the second by Marc Etienne Brachet refers to the bifurcations arising in attractive Bose-Einstein condensates and superfluid helium and the third course by André Verbeure is a pedagogical introduction to the subject with special emphasis on first principles and rigorous results. Part I is completed by two courses given by Michel Moreau: the first one on diffusion limited reactions of particles with fluctuating activity and the second on the phase boundary dynamics in a one dimensional nonequilibrium lattice gas. Part II includes a selection of invited seminars at both Workshops.Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to instabilities leading to nonlinear oscillations. We study numerically this equation set within a particular range of parameters, and find uniformly propagating localized objects behaving as coherent structures. Some of the localized objects found are interpreted in terms of exact analytical solutions.We acknowledge financial support from Programa de Desarrollo de Ciencias Básicas (PEDECIBA, Uruguay), Comisión Sectorial de Investigación Científica (CSIC, Uruguay), and MCyT (Spain) project CONOCE BFM2000-1108

Fronts between rhythms: Spatiotemporal dynamics of extended polyrhythmic media

4 pages.-- PACS numbers: 05.45.Gg.-- Final full-text version of the paper available at: http://dx.doi.org/10.1103/PhysRevLett.99.174101.This work was funded by Spanish MEC Grants No. CTQ2004-04648, No. FIS2005-07083-C02-02, sabbatical funds for O. P., CSIC project HIELOCRIS, and Brazilian agencies CNPq and FAPERN