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Georg Börner1, Hauke Haehne2, Jose Casadiego1

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Inferring the state space dimension of complex dynamical systems is now possible using just one time series observation. This method works for systems with up to 100 variables, offering new insights into system dynamics.

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Area of Science:

  • Complex Systems
  • Dynamical Systems Theory
  • Network Science

Background:

  • Most natural and human-made systems are complex and networked, evolving over time.
  • The state space dimension is a fundamental property of these systems but is difficult to determine.
  • Previous methods required observing a fraction of variables to infer system dimension.

Purpose of the Study:

  • To demonstrate that time series data from a single variable is sufficient for inferring the state space dimension.
  • To identify practical constraints and experimental choices affecting the accuracy of dimension inference.
  • To provide guidelines for effective data collection in complex systems.

Main Methods:

  • Mathematical formulation for dimension inference using a single time series.
  • Evaluation of numerical constraints and experimental parameters (sampling interval, observation duration).
  • Testing the method on networked dynamical systems with N=10 to N=100 variables.

Main Results:

  • Time series observations of a single variable are mathematically sufficient for state space dimension inference.
  • Successful inference is sensitive to numerical precision, sampling intervals, and observation duration.
  • Robust inference demonstrated for systems up to 100 variables using single-variable data.

Conclusions:

  • A simplified approach using single-variable time series enables state space dimension inference in complex networked systems.
  • The accuracy of inference depends critically on data quality, quantity, and experimental design.
  • This work offers practical guidance for measuring and analyzing complex dynamical systems.