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Crisis in Time-Dependent Dynamical Systems.

Simona Olmi1,2, Antonio Politi1,3

  • 1Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.

Physical Review Letters
|April 25, 2025
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Summary
This summary is machine-generated.

This study investigates crises in dynamical systems operating in fluctuating environments. We found a novel scaling law for escape probability near critical points, verified in systems like the Kuramoto model.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Dynamical systems often operate in fluctuating environments, leading to complex behaviors.
  • Transitions and bifurcations in these systems remain incompletely understood, particularly crises.

Purpose of the Study:

  • To investigate the occurrence and mechanisms of crises in nonautonomous dynamical systems.
  • To derive and verify a scaling law for escape probability near crisis points.

Main Methods:

  • Analysis of crises in low-dimensional dynamical systems.
  • Derivation of the escape probability scaling law near the critical point.
  • Numerical verification in various systems, including the Kuramoto model with inertia.

Main Results:

  • Crises, characterized by phase space flooding, occur in nonautonomous systems.
  • Escape probability near the critical point scales as exp[-α(lnδ)^{2}].
  • The parameter α is dependent on the specific dynamical system model.

Conclusions:

  • The derived scaling law provides a quantitative description of crisis dynamics in nonautonomous systems.
  • The findings are relevant to understanding phenomena like the loss of stability in chimera states.