Calculated Attractor Dimensions for Low-Order Spectral Models

Publisher Website
Google Scholar
Abstract
Advancing knowledge about the phase space topologies of nonlinear hydrodynamic or dynamical systems has raised the question of whether the structure of the attractors in which the solutions are eventually confined can be characterized rigorously and economically. It is shown by applying the Lyapunov exponents, Lyapunov dimension, and correlation dimension to several low-order truncated spectral models that these quantities give useful information about the phase space structure and predictability characteristics of such attractors. The Lyapunov exponents measure the average exponential rate of convergence or divergence of nearby solution trajectories in an appropriate phase space. The Lyapunov dimension dL incorporates the dynamical information of the Lyapunov exponents to give an estimate of the dimension of the system attractor, while the correlation dimension v is a more geometrically motivated measure that is simple to compute and related to more classical dimensions. The Lyapunov exponents d... Abstract Advancing knowledge about the phase space topologies of nonlinear hydrodynamic or dynamical systems has raised the question of whether the structure of the attractors in which the solutions are eventually confined can be characterized rigorously and economically. It is shown by applying the Lyapunov exponents, Lyapunov dimension, and correlation dimension to several low-order truncated spectral models that these quantities give useful information about the phase space structure and predictability characteristics of such attractors. The Lyapunov exponents measure the average exponential rate of convergence or divergence of nearby solution trajectories in an appropriate phase space. The Lyapunov dimension dL incorporates the dynamical information of the Lyapunov exponents to give an estimate of the dimension of the system attractor, while the correlation dimension v is a more geometrically motivated measure that is simple to compute and related to more classical dimensions. The Lyapunov exponents d...

This publication has 0 references indexed in Scilit: