Exact Lyapunov Dimension of the Universal Attractor for the Complex Ginzburg-Landau Equation
- 28 December 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 59 (26) , 2911-2914
- https://doi.org/10.1103/physrevlett.59.2911
Abstract
We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.Keywords
This publication has 11 references indexed in Scilit:
- Coherent structures and chaos: A model problemPhysics Letters A, 1987
- Instabilities of the Ginzburg-Landau equation. II. Secondary bifurcationQuarterly of Applied Mathematics, 1986
- Dynamics of Perturbed Wavetrain Solutions to the Ginzburg‐Landau EquationStudies in Applied Mathematics, 1985
- Global lyapunov exponents, kaplan‐yorke formulas and the dimension of the attractors for 2D navier‐stokes equationsCommunications on Pure and Applied Mathematics, 1985
- Pattern Selection and Spatiotemporal Transition to Chaos in the Ginzburg-Landau EquationPhysical Review Letters, 1983
- Three-Frequency Motion and Chaos in the Ginzburg-Landau EquationPhysical Review Letters, 1982
- Turbulized Rotating Chemical WavesProgress of Theoretical Physics, 1981
- The Eckhaus and Benjamin-Feir resonance mechanismsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- A non-linear instability theory for a wave system in plane Poiseuille flowJournal of Fluid Mechanics, 1971
- Finite bandwidth, finite amplitude convectionJournal of Fluid Mechanics, 1969