Nonlinearly saturated dynamical state of a three-wave mode-coupled dissipative system with linear instability

Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a ge neral set of three-wave mode-coupled ordinary differential equations for co mplex variables. Bounded attractors of the set approximate nonlinearly satu rated turbulent states of real physical systems. Exact criteria for bounded ness of the attractors are found. Fundamentally different kinds of asymptot ic behavior of the wave triad are classified in the parameter space and qua ntitatively assessed.