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Journal of Applied Nonlinear Dynamics 4(1) (2015) 1--9 | DOI:10.5890/JAND.2015.03.001

Rocio E. Ruelas$^{1}$; Richard H. Rand$^{2}$

$^{1}$ Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA

$^{2}$ Department of Mathematics, Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA

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Abstract

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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