We investigate a phenomenon observed in systems of the form

where Pi, Qi and ε are given constants, and where it is assumed that when ε = 0 this system exhibits a pair of linearly independent solutions of period 2π. Since the driver cos2t has period π, we have the ingredients for a 2:1 subharmonic resonance which typically results in a tongue of instability involving unbounded solutions when ε >0. We present conditions on the coefficients Pi, Qi such that the expected instability does not occur, i.e., the tongue of instability has disappeared.

This content is only available via PDF.
You do not currently have access to this content.