On determining the dimension of chaotic flows
Physica D Nonlinear PhenomenaPublished 1 August 1981
Harold Froehling, James P. Crutchfield, Doyne Farmer, Norman H. Packard, R. S. Shaw
Citations159
SJR quartileQ1
SJR score0.94
SNIP1.39
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Abstract
We describe a method for determining the approximate fractal dimension of an attractor. Our technique fits linear subspaces of appropriate dimension to sets of points on the attractor. The deviation between points on the attractor and this local linear subspace is analyzed through standard multilinear regression techniques. We show how the local dimension of attractors underlying physical phenomena can be measured even when only a single time-varying quantity is available for analysis. These methods are applied to several dissipative dynamical systems.
Keywords
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