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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Dynamical systems with multiple long-delayed feedbacks: Multiscale analysis and spatiotemporal equivalence.

Serhiy Yanchuk¹, Giovanni Giacomelli²

¹Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 14, 2015

Summary

This summary is machine-generated.

This study introduces dynamical systems with multiple, hierarchically long-delayed feedback, revealing multiscale dynamics and uncovering hidden patterns like spirals and spatiotemporal chaos through a novel space-time representation.

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Area of Science:

Nonlinear Dynamics
Complex Systems Analysis

Background:

Dynamical systems with delayed feedback are crucial in various scientific fields.
Previous work established foundational concepts for delayed feedback systems.
Understanding multiscale properties in such systems remains a challenge.

Purpose of the Study:

To introduce and study dynamical systems with multiple, hierarchically long-delayed feedback.
To analyze the multiscale properties of a Stuart-Landau oscillator with two feedbacks.
To develop a space-time representation for visualizing complex dynamics.

Main Methods:

Extension of previous work on delayed feedback systems.
Phenomenological modeling using a Stuart-Landau oscillator with two feedbacks.
Derivation of a normal form for systems near destabilization with long delays.
Development and application of a space-time representation.

Main Results:

Demonstration of multiscale properties in the Stuart-Landau oscillator model.
Identification of hidden multiscale patterns, including spirals and spatiotemporal chaos.
Analysis of the influence of delay size on system dynamics and transitions.
Derivation of a normal form for long delays near destabilization.

Conclusions:

The developed space-time representation effectively reveals hidden multiscale patterns in complex dynamical systems.
The study provides insights into the behavior of systems with hierarchical long-delayed feedback.
The method is applicable to systems with multiple delayed feedback terms and offers a framework for further research.