Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation

Abstract

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 regimes encountered. The nature of the transition lines separating these phases is discussed, and preliminary results are presented which aim at evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic limit.

14 pages, LaTeX, 9 figures available by anonymous ftp to amoco.saclay.cea.fr in directory pub/chate, or by requesting them to [email protected]

Cited by in corpus (61)

• The World of the Complex Ginzburg-Landau Equation
• Active Turbulence
• Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
• Semiconductor ring laser frequency combs induced by phase turbulence
• Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation
• The Building Blocks of Spatiotemporal Intermittency
• Characterization of the transition from defect- to phase-turbulence
• Synchronization of Spatiotemporal Chaos: The regime of coupled Spatiotemporal Intermittency
• Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
• Modulated Amplitude Waves and the Transition from Phase to Defect Chaos
• Modulated Amplitude Waves and Defect Formation in the One-Dimensional Complex Ginzburg-Landau Equation
• Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves
• Chimeras in globally coupled oscillatory systems: From ensembles of oscillators to spatially continuous media
• Wound-up phase turbulence in the Complex Ginzburg-Landau equation
• Hyperbolic decoupling of tangent space and effective dimension of dissipative systems
• On the risks of using double precision in numerical simulations of spatio-temporal chaos
• Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation
• Feedback Control of Traveling Wave Solutions of the Complex Ginzburg Landau Equation
• Turbulence-induced rogue waves in Kerr resonators
• Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex Ginzburg-Landau equation
• Hole Solutions in the 1d Complex Ginzburg-Landau Equation
• Noise induced transition from an absorbing phase to a regime of stochastic spatiotemporal intermittency
• Order Parameter for the Transition from Phase to Amplitude Turbulence
• Numerical Study of a Lyapunov Functional for the Complex Ginzburg-Landau Equation
• Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
• Synchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems
• Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation
• Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice
• Nonlinear Analysis of the Eckhaus Instability: Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient
• Dynamic characterisers of spatiotemporal intermittency
• The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings
• Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions
• Dissipative Dynamics of an Open Bose Einstein Condensate
• Spatiotemporal Chaos, Localized Structures and Synchronization in the Vector Complex Ginzburg-Landau Equation
• Identification of parameters in amplitude equations describing coupled wakes
• Self-Stabilization Mechanism in Ultra-Stable Fourier Domain Mode-Locked (FDML) Lasers
• Self-induced Faraday instability laser
• Phase Instability as a Source of Modal Dynamics in Semiconductor Lasers
• Turbulence near cyclic fold bifurcations in birhythmic media
• Nonequilibrium Dynamics of the Complex Ginzburg-Landau Equation. I. Analytical Results
• A quasi-periodic route to chaos in a parametrically driven nonlinear medium
• Analytic expressions of hydrothermal waves
• Hole-defect chaos in the one-dimensional complex Ginzburg-Landau equation
• Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
• Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
• Nonequilibrium Dynamics in the Complex Ginzburg-Landau Equation
• Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate
• Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation
• Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
• Phase diagram of one-dimensional driven-dissipative exciton-polariton condensates
• Wielding Intermittency with Cycle Expansions
• Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation
• Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
• Complex localization mechanisms in networks of coupled oscillators: two case studies
• New solutions to the complex Ginzburg-Landau equations
• Reconstruction of Exciton-Polariton Condensates in 1D Periodic Structures
• Dynamical topology and statistical properties of spatiotemporal chaos
• Independent Component Analysis of Spatiotemporal Chaos
• Beyond the standard approximations: an analysis leading to a correct description of phase instabilities in semiconductor lasers
• All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations
• Pattern formation from Gauge/Gravity Duality