Nonequilibrium statistics of a reduced model for energy transfer in waves

• Published in: Communications on pure and applied mathematics 2007-03, Vol.60 (3), p.439-461
• Main Authors: DeVille, R. E. Lee, Milewski, Paul A., Pignol, Ricardo J., Tabak, Esteban G., Vanden-Eijnden, Eric
• Format: Article
• Language: English
• Subjects: Differential equations; Energy; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Ordinary differential equations; Partial differential equations; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic analysis; Stochastic models; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.20157

We study energy transfer in a “resonant duet”—a resonant quartet where symmetries support a reduced subsystem with only 2 degrees of freedom—where one mode is forced by white noise and the other is damped. We consider a physically motivated family of nonlinear damping forms and investigate their effect on the dynamics of the system. A variety of statistical steady states arise in different parameter regimes, including intermittent bursting phases, states highly constrained by slaving among amplitudes and phases, and Gaussian and non‐Gaussian quasi‐equilibrium regimes. All of this can be understood analytically using asymptotic techniques for stochastic differential equations. © 2006 Wiley Periodicals, Inc.