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Quantifying the complexity of the delayed logistic map.

Cristina Masoller1, Osvaldo A Rosso

  • 1Departament de Física i Enginyeria Nuclear, Escola Tecnica Superior d'Enginyeries Industrial i Aeronautica de Terrassa, Universitat Politècnica de Catalunya, Colom 11, 08222 Terrassa, Barcelona, Spain. cristina.masoller@upc.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 15, 2010
PubMed
Summary
This summary is machine-generated.

This study quantifies the complexity of the delayed logistic map using statistical complexity measures. Two methods, histogram-based and ordinal patterns, offer complementary insights into the system's dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • The delayed logistic map is a model system exhibiting complex dynamics.
  • Quantifying complexity is crucial for understanding nonlinear systems.
  • Existing methods may not capture all facets of system complexity.

Purpose of the Study:

  • To apply and compare two statistical complexity measures to the delayed logistic map.
  • To investigate the complementary nature of histogram-based and ordinal pattern complexity.
  • To analyze the occurrence of forbidden patterns in nonlinear delayed logistic map dynamics.

Main Methods:

  • Calculation of complexity using a histogram-based probability distribution function.
  • Calculation of complexity using ordinal patterns analysis.
  • Analysis of time series generated by linear and nonlinear delayed logistic maps.

Main Results:

  • Histogram-based and ordinal pattern complexity measures provide complementary information.
  • Parameter regions exist where one measure is zero, but the other is not.
  • The nonlinear delayed logistic map can generate time series with no missing or forbidden ordinal patterns.

Conclusions:

  • The chosen complexity measures offer distinct perspectives on the delayed logistic map's dynamics.
  • The interplay between feedback type and parameter choice significantly influences complexity.
  • The realization of all ordinal patterns indicates a specific type of deterministic behavior in the nonlinear system.