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Related Experiment Video

Updated: May 29, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Feigenbaum graphs: a complex network perspective of chaos.

Bartolo Luque¹, Lucas Lacasa, Fernando J Ballesteros

¹Department of Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid, Spain.

|September 15, 2011

Summary

Horizontal visibility graphs offer a new way to study nonlinear systems by converting time series into networks. This method reveals universal properties of dynamical systems, like period-doubling cascades, through "Feigenbaum graphs".

Related Experiment Videos

Last Updated: May 29, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

Complex Systems
Network Science
Dynamical Systems Theory

Background:

The theory of horizontal visibility graphs (HVGs) transforms time series into networks, enabling the study of dynamical systems via network characterization.
This approach offers a graph-theoretical perspective on nonlinear systems, aligning with principles of symbolic dynamics.

Purpose of the Study:

To demonstrate the utility of horizontal visibility graphs in analyzing nonlinear dynamical systems.
To provide a universal analytical description of period-doubling and band-splitting attractors using associated horizontal visibility graphs.

Main Methods:

Application of the horizontal visibility graph (HVG) method to time series generated by unimodal maps.
Development of analytical descriptions for the resulting graphs, termed 'Feigenbaum graphs'.
Analysis of degree distribution and related network properties within the framework of renormalization group theory.

Main Results:

A universal analytical description of period-doubling and band-splitting cascades is established using Feigenbaum graphs, independent of specific map nonlinearities.
Exact results for the degree distribution and network properties of Feigenbaum graphs were derived.
Fixed points of renormalization group analysis coincided with those of network entropy optimization.
Network entropy was shown to mimic the Lyapunov exponent, suggesting a generalized Pesin-like relation.

Conclusions:

Horizontal visibility graphs provide a powerful tool for understanding the dynamics of nonlinear systems.
Feigenbaum graphs offer a universal framework for analyzing classic scenarios like period-doubling cascades.
The study highlights a connection between network entropy and dynamical system properties, extending beyond chaotic regimes.