2003/12/05 by D. Ryvkine, M. I. Dykman, B. Golding · 1 citation
Computer Science · Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Nonlinear Dynamics and Pattern Formation #cond-mat.mes-hall #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.69.061102
18 pages
arxiv created 2003/12/05 · openalex publication_date 2004/06/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Near a bifurcation point a system experiences a critical slowdown. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape W scales with the driving field amplitude A as ln W proportional, variant ( A(c) -A)(xi), where A(c) is the bifurcational value of A. With increasing field frequency the critical exponent xi changes from xi=3/2 for stationary systems to a dynamical value xi=2 and then again to xi=3/2. The analytical results are in agreement with the results of asymptotic calculations in the scaling region. Numerical calculations and simulations for a model system support the theory.