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A symbolic network-based nonlinear theory for dynamical systems observability.

Christophe Letellier1, Irene Sendiña-Nadal2,3, Ezequiel Bianco-Martinez4

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This study introduces a novel method to identify the minimal set of variables for state space reconstruction in complex systems. This approach makes analyzing large-scale networks computationally feasible.

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Area of Science:

  • Systems Biology
  • Network Science
  • Control Theory

Background:

  • Observability is crucial for inferring system states from limited measurements.
  • State space reconstruction in large-scale systems is computationally challenging due to exponential complexity.
  • Existing methods struggle with the high dimensionality of complex networks.

Purpose of the Study:

  • To develop a computationally efficient method for determining system observability in large-scale networks.
  • To identify the minimal set of variables required for accurate state space reconstruction.
  • To enable the analysis of complex real-world systems.

Main Methods:

  • Computing observability coefficients from a symbolic Jacobian matrix.
  • Identifying candidate variables for measurement using the symbolic Jacobian.
  • Calculating symbolic observability coefficients from the symbolic observability matrix.

Main Results:

  • The proposed method successfully identifies the minimal set of variables for state space reconstruction.
  • Results align with analytical computations, validating the approach.
  • The method is applicable to systems with linear, nonlinear polynomial, or rational interactions.

Conclusions:

  • The novel approach significantly reduces the computational burden of observability analysis.
  • This method facilitates the efficient exploration of dynamics in large, complex systems.
  • Promising applications include power grids, socioeconomic networks, and biological networks.