Disappearance of Resonance Tongues
DOI:
https://doi.org/10.5890/JAND.2015.03.001Abstract
We investigate a phenomenon observed in systems of the form dx/dt = a1 (t)x + a2(t)y, dy/dt = a3(t)x + a4(t)y, where ai(t) = 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.References
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