Turbulent Coupled Map Lattices

Abstract

The study of coupled map lattices has become a very fruitful way of building up intuition and knowledge about extended dynamical systems in chaotic states -like hydrodynamical turbulence or inhomogenuos chemical reactions-and testing and generalizing the methods used to describe low-dimensional chaotic systems in a context where spatial degrees of freedom are important. When the word turbulence is used in such systems it does not necessarily imply that we are modelling hydrodynamical systems, nor even that a velocity field is defined. We use the term simply to describe an extended system in a chaotic state, which is spatially disordered as well. As in low-dimensional systems we define a chaotic state as one having a positive Lyapunov exponent, and we then define a turbulent state as one having a number of positive Lyapunov exponents, which grows with the system size, such that this number becomes arbitrarily large for systems large enough.