Rate and noise-induced tipping working in concert

Area of Science:

• Dynamical Systems
• Stochastic Processes
• Statistical Physics

Background:

• Rate-induced tipping describes abrupt shifts between co-existing stable states in dynamical systems driven by a changing parameter.
• Understanding tipping points is crucial for predicting abrupt changes in various complex systems, from climate to ecosystems.

Purpose of the Study:

• To investigate the effect of noise on rate-induced tipping phenomena.
• To identify the most probable pathways for tipping events under the influence of noise.
• To determine if noise can induce tipping at subcritical rates.

Main Methods:

• Analysis of the Freidlin-Wentzell action functional from large deviation theory.
• Identification of a global minimizer representing the most probable tipping path.
• Characterization of this path as a heteroclinic connection for the Euler-Lagrange system.
• Validation through direct Monte Carlo simulations.

Main Results:

• Noise addition enables rate-induced tipping at rates significantly below the critical rate.
• The presence of noise substantially increases the probability of tipping compared to noise acting independently.
• A heteroclinic connection, representing the most probable tipping path, exists for all rates up to the critical rate.

Conclusions:

• Noise plays a critical role in initiating tipping phenomena in dynamical systems, even at low driving rates.
• The identified most probable path provides a theoretical framework for understanding noise-induced tipping.
• Findings have implications for predicting and mitigating abrupt shifts in complex systems.