Instability and Chaos in Non-Linear Wave Interaction: a simple model
  We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above which a loss of stability appears. The dependence of the critical input power on the physical parameters is analyzed. For a driving force with higher amplitude chaotic behavior is observed. Generalization to interactions which include higher modes is discussed.   Keywords: Non-Linear Waves, Stability, Chaos. 
I. M. Khalatnikov and M. Kroyter