Liapounov exponents for the KuramotoSivashinsky model
Abstract
A onedimensional version of the KuramotoSivashinsky (1977, 1978) model was used to examine the transition to stochasticity in deterministic systems. The number of nonnegative values for the Liapunov exponent (LE), a measure of the divergence of neighboring trajectories, is the amount of chaos in the system. The LEs are calculated as the differences between the dimensions of parallelepipeds which undergo either expansion or contraction, i.e., the Haussdorff dimension of the invariant measure on the attractor of the dynamic system. A finite difference second order CrackNicolson/Adams Bashforth scheme was used in simulations of varying LE values in order to characterize the evolution of large scale turbulence phenomena.
 Publication:

Macroscopic Modelling of Turbulent Flows
 Pub Date:
 1985
 DOI:
 10.1007/3540156445_26
 Bibcode:
 1985LNP...230..319M
 Keywords:

 Dynamical Systems;
 Exponents;
 Stochastic Processes;
 Turbulence;
 Chaos;
 CrankNicholson Method;
 Finite Difference Theory;
 Liapunov Functions;
 Parallelepipeds;
 Singularity (Mathematics);
 Fluid Mechanics and Heat Transfer