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A simple model of nonlinear saturation of an unstable mode is studied. The model consists of the resonant three-wave coupling equations with the highest frequency wave linearly unstable and the two lower frequency waves damped. As the damping of the stable waves is increased, the solutions go through an interesting succession of qualitative changes, including bifurcations to increasingly complex periodic solutions and the appearance of apparently chaotic (i.e., aperiodic) solutions. These qualitative features are shown to be explainable on the basis of a one-dimensional mapping which is numerically derivable from the original system of differential equations.
Wersinger et al. (Sun,) studied this question.