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Coordinate Mapping of Hyolaryngeal Mechanics in Swallowing

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Published on: May 6, 2014

Stabilizing embedology: Geometry-preserving delay-coordinate maps.

Armin Eftekhari¹, Han Lun Yap², Michael B Wakin³

¹Alan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, United Kingdom.

Physical Review. E

|March 18, 2018

Summary

This summary is machine-generated.

Delay-coordinate mapping stably embeds nonlinear system attractors by preserving geometry, not just topology. This stability depends on the system

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Area of Science:

Dynamical Systems Theory
Nonlinear Dynamics
Time-Series Analysis

Background:

Delay-coordinate mapping reconstructs system dynamics from time-series data.
Takens' embedding theorem guarantees topological reconstruction but not embedding quality.
Specific parameters influencing reconstruction quality remain unclear.

Purpose of the Study:

Extend Takens' theorem to guarantee stable embeddings.
Preserve attractor geometry, not just topology.
Provide guidance for selecting delay-coordinate mapping parameters.

Main Methods:

Theoretical analysis of delay-coordinate mapping.
Extension of Takens' embedding theorem.
Investigation of conditions for stable embedding.

Main Results:

Delay-coordinate mapping provides a stable embedding if the system's stable rank is proportional to the attractor's dimension.
Stable rank relates sampling interval and number of delays.
Theoretical guidance for parameter selection is established.

Conclusions:

Stable embedding preserves attractor geometry, crucial for accurate analysis.
Findings offer theoretical basis for parameter choices in delay-coordinate mapping.
Results apply to smooth attractors and are extended to strange attractors.