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A simple model for the nonlinear saturation of an instability is studied via numerical solution of the resonant three-wave coupling equations in the case where the high-frequency wave is linearly unstable and the two lower-frequency waves are linearly damped. The solutions are shown to undergo interesting qualitative cahnges as the damping rate of the stable waves is increased. These changes include bifurcations to increasingly complicated periodic motions and the appearance of apparently chaotic motions, possibly indicative of the presence of a strange attractor.
Wersinger et al. (Mon,) studied this question.