Ufa State Petroleum Technical University, 1 Kosmonavtov St., 450062 Ufa, Russia.
Chaos. 2011 Jun;21(2):023109. doi: 10.1063/1.3578047.
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∼ɛ(-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.
我们考虑一个带有小耗散和外部周期微扰的耦合非线性振子的共振微扰系统。我们表明，在大时间 t∼ɛ(-2)时，系统的一个分量主要由非齐次 Mathieu 方程描述，而另一个分量则代表大振幅的脉动。得到了一个哈密顿系统，它在特殊情况下主要描述了包络的行为。解析结果与数值模拟相符。
