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Forced nonlinear resonance in a system of coupled oscillators. (English) Zbl 1317.34054

Summary: We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time \(t\sim\varepsilon^{-2}\) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.{
©2011 American Institute of Physics}

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D10 Perturbations of ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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