Nonequilibrium statistics of a reduced model for energy transfer in waves

R. E.Lee DeVille, Paul A. Milewski, Ricardo J. Pignol, Esteban G. Tabak, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)439-461
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Issue number3
StatePublished - Mar 2007

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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