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

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.