2006/11/30 by Nils Berglund, Bastien Fernandez, Barbara Gentz · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics #math-ph #math.DS #math.MP #math.PR #msc:37G40 #msc:37H20 #msc:37L60 #msc:60K35
paper · pdf · doi:10.1088/0951-7715/20/11/006
published as Nonlinearity 20, 11 (2007) 2551-2581
arxiv created 2007/07/06 · openalex publication_date 2007/10/04 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. The system shows a metastable behaviour, which is characterized by the location and stability of its equilibrium points. We show that as the coupling strength increases, the number of equilibrium points decreases from 3 N to 3. While for weak coupling, the system behaves like an Ising model with spin-flip dynamics, for strong coupling (of the order N 2 ), it synchronizes, in the sense that all particles assume almost the same position in their respective local potential most of the time. We derive the exponential asymptotics for the transition times, and describe the most probable transition paths between synchronized states, in particular for coupling intensities below the synchronization threshold. Our techniques involve a centre-manifold analysis of the desynchronization bifurcation, with a precise control of the stability of bifurcating solutions, allowing us to give a detailed description of the system's potential landscape.