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Predicting collapse of adaptive networked systems without knowing the network.

Leonhard Horstmeyer1,2, Tuan Minh Pham1,2, Jan Korbel1,2

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This summary is machine-generated.

Network collapses in ecosystems and economies can be predicted using non-structural data. A "quantization effect" in node states signals impending instability, offering an early warning for system collapse.

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Area of Science:

  • Complex systems science
  • Network theory
  • Dynamical systems

Background:

  • Network collapses in ecosystems, species extinction, and economic breakdown are often linked to network topology and feedback cycles.
  • Predicting these collapses typically requires detailed structural information, which is often unavailable.

Purpose of the Study:

  • To develop a method for predicting network collapse using only non-structural information.
  • To identify an early warning signal for system instability.

Main Methods:

  • Utilizing a corollary of the Perron-Frobenius theorem to detect directed cycles.
  • Analyzing non-structural node state data (e.g., species abundances, company revenues).
  • Applying linear or linearized dynamics to model system behavior.

Main Results:

  • A "quantization effect" in node states serves as an early warning signal for network collapse.
  • This signal is detectable without requiring detailed structural network information.
  • The method is validated in co-evolutionary ecosystem models and applicable to epidemiology and population dynamics.

Conclusions:

  • Network collapse prediction is possible for systems with linear dynamics using readily available, non-structural data.
  • The "quantization effect" provides a universal early warning signal for structural instability in complex networks.