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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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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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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics.

Guangyu Yang1, Daolin Xu1, Haicheng Zhang1

  • 1State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study introduces a new recurrence network analysis to track dynamical systems. The method effectively differentiates healthy individuals from ventricular tachycardia patients using time series data.

Keywords:
chaoscomplex networktime series analysis

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Area of Science:

  • Complex Systems Analysis
  • Network Science
  • Time Series Analysis

Background:

  • Dynamical systems analysis often relies on complex mathematical models.
  • Characterizing the evolution of time series data presents significant challenges.
  • Recurrence networks offer a novel approach to visualizing and analyzing system dynamics.

Purpose of the Study:

  • To propose a new analysis method for characterizing dynamical system evolution using recurrence networks.
  • To introduce novel statistical measures for unraveling signal evolution properties.
  • To demonstrate the robustness and applicability of the method in distinguishing physiological states.

Main Methods:

  • Phase space reconstruction to transform time series into high- and low-dimensional recurrence networks.
  • Calculation of correlation coefficient of node degrees (CCND) and edge similarity.
  • Analysis of CCND decline rates and edge similarity fluctuations.
  • Testing robustness against additive noise and application to clinical data.

Main Results:

  • Distinct CCND decline patterns observed across different network dimensions and dynamics.
  • Emergence of exponential scaling in CCND for chaotic time series.
  • Edge similarity provides detailed characterization of dynamical systems.
  • The proposed CCND and edge similarity measures are robust to additive noise.
  • Successful differentiation between healthy subjects and ventricular tachycardia patients.

Conclusions:

  • The recurrence network analysis method effectively characterizes dynamical system evolution.
  • CCND and edge similarity are robust and informative statistical measures.
  • The method demonstrates significant potential for clinical applications, such as in diagnosing cardiac arrhythmias.