Related papers: Phase chaos in the anisotropic complex Ginzburg-La…
I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered…
After a brief introduction to the complex Ginzburg-Landau equation, some of its important features in two space dimensions are reviewed. A comprehensive study of the various phases observed numerically in large systems over the whole…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
Spatio-temporal chaos in parametrically driven waves is investigated in one and two dimensions using numerical simulations of Ginzburg-Landau equations. A regime is identified in which in one dimension the dynamics are due to double phase…
We present results of numerical simulations of coupled Ginzburg-Landau equations that describe parametrically excited waves. In one dimension we focus on a new regime in which the Eckhaus sideband instability does not lead to an overall…
The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity,…
The anisotropic complex Ginzburg-Landau equation (ACGLE) describes slow modulations of patterns in anisotropic spatially extended systems near oscillatory (Hopf) instabilities with zero wavenumbers. Traveling wave solutions to the ACGLE…
A two-dimensional system of non-locally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As already known for the one-dimensional case, the system exhibits anomalous spatio-temporal chaos…
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…
In a Ginzburg-Landau model for parametrically driven waves a transition between a state of ordered and one of disordered spatio-temporal defect chaos is found. To characterize the two different chaotic states and to get insight into the…
The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…
We study the dynamics of holes and defects in the 1D complex Ginzburg--Landau equation in ordered and chaotic cases. Ordered hole--defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects…
We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly…
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…
The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order…
We consider phase turbulent regimes with nonzero winding number in the one-dimensional Complex Ginzburg-Landau equation. We find that phase turbulent states with winding number larger than a critical one are only transients and decay to…
Noise power spectra in spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the temporal noise spectra are of…
Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary…
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…
Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and…