2001/11/13 by Nils Berglund, NILS BERGLUND, Barbara Gentz +1 · 1 citation
Environmental Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Ecosystem dynamics and resilience #nlin.CD #physics.ao-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1142/s0219493702000455
published as Stoch. Dyn. 2:327-356 (2002) · 24 pages, 8 figures. Proceedings of the "Second Workshop on Stochastic Climate Models", Chorin, 9-11 July, 2001
arxiv created 2001/11/13 · openalex publication_date 2002/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium, instead of adiabatically following the stationary distribution of the frozen system. This behavior can be characterized by describing the location of typical paths, and bounding the probability of atypical paths. We illustrate this approach by giving a quantitative description of phenomena associated with bistability, for three famous examples of simple climate models: Stochastic resonance in an energy balance model describing the Ice Ages; hysteresis in a box model for the Atlantic thermohaline circulation; and bifurcation delay in the case of the Lorenz model for Rayleigh–Bénard convection.