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Noise-induced desynchronization and stochastic escape from equilibrium in complex networks.

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External noise can cause complex physical systems to leave their stable state. This study derives conditions for this stochastic escape, finding systems with inertia may escape faster, contrary to intuition.

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Area of Science:

  • Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Complex physical systems are modeled by differential equations but are affected by external environments.
  • These environmental effects are represented as noise terms, which can destabilize systems.
  • Understanding system behavior under perturbation is crucial for predicting stability.

Purpose of the Study:

  • To derive conditions for stochastic escape from a stable equilibrium in complex systems under noise perturbations.
  • To investigate the role of inertia in the rate of basin escape.
  • To validate theoretical findings through numerical simulations on various network structures.

Main Methods:

  • Derivation of analytical conditions for stochastic escape based on system dynamics and noise levels.
  • Focus on Kuramoto-like models for coupled oscillators.
  • Numerical simulations on four distinct complex networks to confirm theoretical predictions.

Main Results:

  • Established criteria for noise-induced stochastic escape from the basin of attraction.
  • Demonstrated that systems with inertia can escape their initial basin faster than or equal to systems without inertia.
  • Identified exceptions to this finding, particularly under strong white-noise perturbations.

Conclusions:

  • The derived conditions provide a framework for predicting noise-induced transitions in complex systems.
  • The counterintuitive finding regarding inertia suggests a need for re-evaluation of system design and control strategies.
  • Numerical validation across diverse networks supports the general applicability of the findings.