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Related Experiment Video

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How to Build a Dichoptic Presentation System That Includes an Eye Tracker

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Published on: September 6, 2017

Checkerboard maps.

N. J. Balmforth¹, E. A. Spiegel, C. Tresser

¹Department of Astronomy, Columbia University, New York, New York 10027IBM T. J. Watson Laboratories, Yorktown Heights, New York 10598.

Chaos (Woodbury, N.Y.)

|March 1, 1995

Summary

This summary is machine-generated.

Researchers propose approximating complex dynamical systems with a positive Lyapunov exponent using finite sets of curves. This method models the system

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Area of Science:

Dynamical Systems and Chaos Theory
Nonlinear Dynamics

Background:

Attractors in systems with one positive Lyapunov exponent often exhibit complex, spaghetti-like structures.
Deterministic jumping between these structures complicates analysis.

Purpose of the Study:

To develop a novel approximation method for complex attractors in dynamical systems.
To represent these attractors as finite sets of curves for easier analysis.

Main Methods:

Approximating attractors as finite sets of K parametrized curves.
Defining a map that transforms a set of curves into itself.
Graphing the map on a KxK checkerboard as a discontinuous one-dimensional map.

Main Results:

The proposed method captures the quantitative dynamics of the original system.
The approximation's accuracy increases with a larger number of curves (K).
The system's dynamics are represented by a discontinuous one-dimensional map.

Conclusions:

Finite sets of curves provide an effective approximation for complex attractors.
This approach simplifies the study of deterministic jumping in chaotic systems.
The checkerboard graph offers a new perspective on visualizing dynamical system behavior.