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Intermittent dynamics in complex systems driven to depletion.

Juan V Escobar1, Isaac Pérez Castillo2,3

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Complex systems depleted by external factors exhibit intermittent dynamics. This study proposes a predictive model based on energy density thresholds, revealing predictable avalanches in complex systems, including social dynamics.

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Network Science

Background:

  • Complex systems driven to depletion often display intermittent dynamics, characterized by periods of calm punctuated by catastrophic bursts.
  • Understanding and predicting these dynamics are crucial for managing risks in various natural and social systems.

Purpose of the Study:

  • To propose a novel mechanism explaining intermittent dynamics in complex systems driven to depletion.
  • To develop a model capable of predicting catastrophic events (avalanches) despite the inherent stochasticity.
  • To demonstrate the model's applicability to both natural and social complex systems.

Main Methods:

  • Development of a theoretical model based on sharp thresholds of local generalized energy density.
  • Analysis of the transition from continuous to intermittent dynamics.
  • Stochastic process modeling to predict avalanche behavior.
  • Validation against empirical data from a real social system.

Main Results:

  • A transition from continuous to intermittent dynamics was identified.
  • The model successfully predicts avalanches, even within a stochastic framework.
  • The proposed mechanism accurately describes the time evolution and avalanche patterns in a real social system.
  • The model highlights the role of negative feedback in regulating system dynamics.

Conclusions:

  • The proposed energy density threshold model provides a unified mechanism for intermittent dynamics in complex systems.
  • Predictability of catastrophic events is achievable by understanding underlying threshold dynamics.
  • The model has broad applicability, offering insights into resource depletion, system failures, and social dynamics.