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Type-I intermittency from Markov binary block visibility graph perspective.

Pejman Bordbar1, Sodeif Ahadpour1

  • 1Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.

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|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study analyzes type-I intermittency using visibility graphs, identifying distinct laminar and non-laminar phases. These phases and regions are characterized and statistically analyzed, offering insights into complex system dynamics.

Keywords:
Markov binary visibility graphType-I intermittencybinary block designchaos

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Theory

Background:

  • Type-I intermittency is a phenomenon observed in nonlinear systems, characterized by alternating laminar and turbulent phases.
  • Visibility graphs offer a novel approach to analyze time series data by converting them into complex networks.

Purpose of the Study:

  • To investigate type-I intermittency using optimized Markov binary visibility graphs.
  • To characterize and classify the distinct phases and regions within the laminar and non-laminar zones of type-I intermittency.
  • To analyze the statistical properties of these phases and regions and their corresponding complex network structures.

Main Methods:

  • Utilizing the logistic map as a model for type-I intermittency.
  • Applying optimized Markov binary visibility graphs to time series data.
  • Employing statistical tools to analyze laminar zone properties (e.g., maximum length, mean length, length distributions).
  • Investigating the degree distribution of the generated complex networks.

Main Results:

  • Identified and defined five distinct phases for the laminar zone: pure, switching, threshold, trapping, and transforming.
  • Defined three distinct regions for the non-laminar zone: initial, terminal reinjection, and chaotic burst.
  • Characterized the statistical properties of these phases and regions.
  • Proposed theoretical degree distributions to predict the behavior of these phases and regions.

Conclusions:

  • Visibility graph analysis provides a robust framework for understanding the complex dynamics of type-I intermittency.
  • The identified phases and regions offer a detailed characterization of intermittency transitions.
  • The study demonstrates the predictive power of network-based analysis for nonlinear phenomena.