The liapunov dimension of strange attractors

Predicting the dimension of strange attractors

The correlation dimension was calculated for a collection of 6080 strange attractors obtained numerically from low-degree polynomial, low-dimensional maps and flows. It was found that the average correlation dimension scales approximately as the square root of the dimension of the system with a surprisingly small variation. This result provides an estimate of the number of dynamical variables r...

Dimension of Time in Strange Attractors

In the rendering of strange attractors a number of methods are outlined how the element of time can be used. Time can be represented as the number of times a mapped location is selected or when the location is selected. A variety of coloring schemes based on the concept of time are also discussed. The other aspect time serves is the ability to visually suggest three-dimensional surfaces within ...

Mutual information, strange attractors, and the optimal estimation of dimension.

Strange attractors

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Characterizing strange nonchaotic attractors.

Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Second, we propose to characterize their strangeness by calculating a phase sensitivity exponent, that measures the...