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Related Experiment Video

Updated: May 10, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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

Published on: December 7, 2021

Horizontal visibility graphs generated by type-I intermittency.

Ángel M Núñez1, Bartolo Luque, Lucas Lacasa

  • 1Dept. Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

This study uses horizontal visibility (HV) graph theory to analyze type-I intermittency in chaotic systems. The research reveals how graph structures reflect chaotic dynamics, linking network parameters to system behavior.

Related Experiment Videos

Last Updated: May 10, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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 Theory
  • Dynamical Systems

Background:

  • Type-I intermittency is a route to chaos characterized by alternating laminar and chaotic phases.
  • Horizontal visibility (HV) graph theory provides a method to analyze time series by constructing graphs based on visibility criteria.

Purpose of the Study:

  • To investigate the type-I intermittency route to chaos using horizontal visibility (HV) graph theory.
  • To establish a connection between the dynamics of unimodal maps and the structural properties of their associated HV graphs.
  • To develop a theoretical framework for understanding intermittency through network parameters.

Main Methods:

  • Generating time series from unimodal maps near a tangent bifurcation.
  • Constructing horizontal visibility (HV) graphs from these time series.
  • Analyzing network parameters such as degree distribution and block entropy.
  • Applying a renormalization-group framework to the HV graphs.

Main Results:

  • The alternation of laminar episodes and chaotic bursts leaves a distinct fingerprint on the HV graph structure.
  • A phenomenological theory successfully predicts network parameters, showing that power-law scaling in laminar lengths is inherited by the graph degree distribution variance.
  • Power-law scaling of the Lyapunov exponent is mirrored in the scaling of block entropy functionals within the HV graphs.
  • A renormalization-group framework for HV graphs identifies fixed points corresponding to different dynamics, with the tangency condition linked to a nontrivial fixed point.

Conclusions:

  • HV graph theory offers a powerful tool to characterize and quantify intermittent dynamics in chaotic systems.
  • The study demonstrates a direct mapping between dynamical system properties and network topological features.
  • The developed renormalization-group approach provides insights into the classification of dynamical behaviors based on graph properties.