Forced Nonlinear Resonance in a System of Coupled Oscillators

We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim ε^{-2}$ 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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