We investigate a phenomenon observed in systems of the form  
dx/dt=a1tx+a2ty
 
dy/dt=a3tx+a4ty
where  
ait=Pi+εQicos2t

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.

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