Non–equilibrium statistics of a reduced model for energy transfer in waves

We study energy transfer in a “resonant duet” — a resonant quartet where symmetries support a reduced subsystem with only two 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, non–equilibrium 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.