Forced Nonlinear Resonance in a System of Coupled Oscillators

Details Forced Nonlinear Resonance in a System of Coupled Oscillators Forced Nonlinear Resonance in a System of Coupled Oscillators

2010-12-08

arxiv.org/abs/1012.1758v1

Physics

Mathematical Physics

17 pages, 11 figures

Scientific paper

We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim \epsilon^{-2}$ one component of the system is described in the main by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes the behaviour of the envelope in the main. The analytic results agree to numerical simulations.

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