THE STABILITY OF PARAMETRICALLY FORCED COUPLED OSCILLATORS IN SUM RESONANCE

For a system of two damped parametrically forced oscillators in sum re sonance the planar stability diagram of amplitude versus frequency of the forcing shows a discontinuity at damping zero, This is a well know n phenomenon, for which we give a geometrical explanation. A linear st ability analysis suffices. We show that a versal (i.e. a structurally stable) matrix unfolding for this problem needs four parameters, indic ating that the stability diagram is actually four dimensional., The bo undary of the stability region in parameter space is singular, this pr ovides a geometric explanation of the discontinuity in the planar stab ility diagram.