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 $t \sim \epsilon^{-2}$ 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.