Abstract
The equations governing the nonlinear interaction of three resonant waves are studied in the limit that one wave is slightly unstable, and the other two modes more heavily damped. It is shown that the dynamics can be described in terms of a bimodal one-dimensional map, which allows bifurcation sequences etc. to be simply constructed. The effect of small additive noise can be studied in the same framework; it is shown that, even at very low levels, the effect of noise can be extremely important in determining the period and amplitude of the oscillations.
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