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Statistical complexity of the time dependent damped L84 model.

Á Fülöp1

  • 1Department of Computer Algebra, University Eötvös Loránd University, Pázmány Péter street 1/C, 1117 Budapest, Hungary.

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Summary

Statistical complexity analysis using snapshot attractors reveals the behavior of time-dependent damped systems. This method distinguishes regular, random, and structural complexity in dynamical systems like the L84 model.

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Area of Science:

  • Dynamical Systems Theory
  • Statistical Physics
  • Chaos Theory

Background:

  • Understanding the behavior of time-dependent damped systems is crucial in various scientific fields.
  • Traditional methods struggle to differentiate between regular, random, and complex dynamics in finite simulations.
  • Snapshot attractors offer a novel approach to analyzing system dynamics over time.

Purpose of the Study:

  • To introduce and apply the concept of statistical complexity using snapshot attractors for time-dependent damped systems.
  • To differentiate between regular, random, and structural complexity in dynamical systems.
  • To analyze the chaotic behavior of the L84 model under periodic damping.

Main Methods:

  • Utilizing snapshot attractors to represent the state of dynamical systems at specific times.
  • Analyzing the probability distribution of points on the Poincaré section of the snapshot attractor.
  • Calculating statistical complexity based on the observed probability distributions.
  • Investigating the L84 model with periodic damping across a range of standard parameter values.

Main Results:

  • Statistical complexity effectively distinguishes between regular, random, and complex dynamics in finite simulations.
  • The L84 model exhibits chaotic behavior, quantifiable through statistical complexity on its snapshot attractor.
  • Periodic damping influences the statistical complexity and overall dynamics of the L84 model.
  • The probability distribution on the Poincaré section provides insights into system complexity.

Conclusions:

  • Snapshot attractors combined with statistical complexity offer a powerful tool for analyzing time-dependent damped systems.
  • This approach provides a robust method for characterizing the complexity of dynamical systems, including chaotic ones.
  • The findings highlight the impact of periodic damping on system dynamics and complexity, particularly in the L84 model.