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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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A variable threshold for recurrence based on local attractor density.

Rémi Delage¹, Toshihiko Nakata¹

¹Department of Management Science and Technology, Tohoku University, Sendai 980-8579, Japan.

Chaos (Woodbury, N.Y.)

|October 1, 2022

Summary

This study introduces a new recurrence plot definition using local attractor density for dynamical systems analysis. This method improves recurrence plot quality and robustness to noise and threshold variations.

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Area of Science:

Dynamical Systems Analysis
Nonlinear Dynamics
Time Series Analysis

Background:

Recurrence plots (RPs) and their quantification measures are valuable tools for studying dynamical systems.
The choice of distance threshold in RPs significantly impacts observed structures and measures.
Optimizing the distance threshold is critical for accurate dynamical system analysis.

Purpose of the Study:

To propose a novel definition of recurrence based on local attractor density.
To generate more qualitative recurrence plots that capture dynamics across scales.
To improve robustness against tangential motion effects and noise.

Main Methods:

A new recurrence definition based on local attractor density was developed.
The proposed method was qualitatively and quantitatively compared with traditional thresholding techniques.
A modification was introduced to enhance noise robustness.

Main Results:

The suggested recurrence plot definition yields more uniform line structures.
The new method demonstrates reduced sensitivity to the distance threshold parameter.
The modified approach shows enhanced robustness when analyzing noisy signals.

Conclusions:

The local attractor density-based recurrence definition offers improved qualitative and quantitative analysis of dynamical systems.
This method provides more stable and informative recurrence plots compared to standard thresholding.
The enhanced robustness to noise makes it suitable for real-world, imperfect data.