Nonequilibrium 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 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.