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Information Transfer Among the Components in Multi-Dimensional Complex Dynamical Systems.

Yimin Yin1, Xiaojun Duan1

  • 1College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410072, China.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study establishes a formalism for information transfer in dynamic systems, quantifying uncertainty for better prediction and control. It analyzes entropy changes to understand complex system dynamics.

Keywords:
Chua’s systemInformation transferLorenz systemcontinuous flowdiscrete mapping

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Area of Science:

  • Complex Systems Dynamics
  • Information Theory
  • Nonlinear Dynamics

Background:

  • Understanding information flow is crucial for analyzing complex systems.
  • Existing methods often lack a unified formalism for multi-dimensional systems.
  • Entropy change provides a fundamental basis for quantifying information dynamics.

Purpose of the Study:

  • To establish a rigorous formalism for information transfer in multi-dimensional deterministic dynamic systems.
  • To generalize the analysis of information transfer to high-dimensional systems.
  • To quantify information transfer uncertainty for dynamic sensitivity analysis.

Main Methods:

  • Derivation of information transfer mechanisms from entropy change and transfer.
  • Development of explicit formulas for continuous flows and discrete mappings.
  • Verification of formulas using the Lorenz and Chua's systems.

Main Results:

  • A generalized formalism for information transfer in deterministic dynamic systems.
  • Quantification of information transfer uncertainty across system variables.
  • Demonstrated applicability to classical systems like Lorenz and Chua's.

Conclusions:

  • The developed formalism provides a robust framework for analyzing information transfer in complex systems.
  • Quantified uncertainty enables statistical dynamic sensitivity analysis.
  • The approach aids in understanding, prediction, and control across diverse scientific fields.