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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Characterizing system dynamics with a weighted and directed network constructed from time series data.

Xiaoran Sun1, Michael Small2, Yi Zhao1

  • 1Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces a new method to convert time series data into weighted, directed networks. This network analysis reveals underlying system dynamics and identifies transitions by examining loop structures.

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Area of Science:

  • Complex Systems
  • Network Science
  • Time Series Analysis

Background:

  • Time series analysis often requires advanced methods to capture complex dynamics.
  • Network theory provides powerful tools for analyzing interconnected systems.
  • Symbolic representations are useful for simplifying complex data patterns.

Purpose of the Study:

  • To develop a novel method for transforming time series data into weighted, directed networks.
  • To encode the underlying dynamics of a time series within its network structure.
  • To demonstrate the utility of this network approach for detecting dynamical transitions and characterizing system behavior.

Main Methods:

  • A sliding window approach is used to segment time series data.
  • A doubly symbolic scheme combines amplitude and ordinal pattern information for segment characterization.
  • Network nodes represent symbol-pairs, and directed links denote temporal succession.
  • A random walk algorithm is employed to sample network loops.

Main Results:

  • Network measures effectively detect dynamical transitions in benchmark systems.
  • The network structure encodes the underlying dynamics of the time series.
  • Distinct loop structures in the networks correlate with different time series dynamics.
  • The relative prevalence of loops of varying lengths can identify underlying dynamics.

Conclusions:

  • The proposed time series to network transformation method is effective for analyzing complex systems.
  • Network-based analysis, particularly loop structure, offers a novel way to understand time series dynamics.
  • This method provides a robust framework for detecting system transitions and classifying dynamics.