耦合振子系统的强迫非线性共振
Forced Nonlinear Resonance in a System of Coupled Oscillators
摘要：
考虑一类具有小耗散和外部周期扰动的耦合非线性振子共振摄动系统。我们表明，对于大的时间$t \sim ε^{-2}$的一个组成部分的系统中描述的主要由非齐次马蒂厄方程，而另一个组成部分代表大振幅的脉动。一个哈密顿系统，它描述的行为的信封中的主要。分析结果与数值模拟结果一致。
英文摘要：
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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