We propose a model for the dynamics of spin-wave instabilities driven by a rf field perpendicular to the dc magnetic field in the second- order Suhl process. We show that a self-oscillation arises from the dynamic nonlinear interaction between the k=0 mode driven by the pumping field and a degenerate k≠0 magnon, with frequency that depends on the dissipation rates and the nonlinear interaction parameters and not on the sample dimensions. For certain parameter values, as the driving field increases we find a period-doubling route to chaos and odd-period bifurcation windows consistent with recent experiments in yttrium iron garnet
