论文标题
在两频的准周期性扰动上，系统接近二维哈密顿量的系统扰动
On two-frequency quasi-periodic perturbations of systems close to two-dimensional Hamiltonian ones with a double limit cycle
论文作者
论文摘要
在相应的扰动自主系统具有双重限制周期的情况下，研究了两频准周期扰动对接近任意非线性二维汉密尔顿的系统的影响。它的解决方案对于非线性振荡的同步和动力学系统分叉理论都很重要。在具有准周期性扰动频率的未扰动系统的固有频率的可相当性的情况下，会发生共振。得出了平均系统，可以确定共振区的结构，即描述在单个共振水平附近的解决方案的行为。对这些系统的研究允许确定当谐振水平偏离未扰动系统的水平时，会产生可能的分叉，该系统在扰动的自主系统中产生双重限制周期。获得的理论结果应用于两种频率的准扰动摆型方程，并通过数值计算说明。
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit cycle. Its solution is important both for the theory of synchronization of nonlinear oscillations and for the theory of bifurcations of dynamical systems. In the case of commensurability of the natural frequency of the unperturbed system with frequencies of quasi-periodic perturbation, resonance occurs. Averaged systems are derived that make it possible to ascertain the structure of the resonance zone, that is, to describe the behavior of solutions in the neighborhood of individual resonance levels. The study of these systems allows determining possible bifurcations arising when the resonance level deviates from the level of the unperturbed system, which generates a double limit cycle in a perturbed autonomous system. The theoretical results obtained are applied in the study of a two-frequency quasi-periodic perturbed pendulum-type equation and are illustrated by numerical computations.
