两个耦合Van der Pol振子系统的一阶近似守恒量

用直接积分法计算两个耦合Van der Pol振子系统的一阶近似守恒量,将两个耦合Van der Pol振子系统看成是未受微扰系统与微扰项的迭加,先通过坐标变换将未受微扰系统解耦,并对解耦系统的3种可能状态进行讨论,得到未受微扰系统的13个精确守恒量,再考虑微扰项对精确守恒量的影响,运用一阶近似守恒量的性质,得到1个稳定的一阶近似守恒量.另外,由13个精确守恒量直接得到13个平凡的一阶近似守恒量.

First order approximate conserved quantities of two coupled Van der Pol oscillators system

The first order approximate conserved quantities of two coupled Van der Pol oscillators system is investigated by using direct integral method. Two coupled Van der Pol oscillators system is taken as the combination of unperturbed system and perturbed terms. Firstly, the unperturbed system is decoupled by transforming coordinates, and thirteen exact conserved quantities of unperturbed system are obtain by discussing the three possible condition of uncoupled system. Second, the influence of perturbed terms on exact conserved quantities is examined. Finally, a stable first order approximate conserved quantity of the system is developed according to the characteristic of the first order approximate conserved quantities. In additional, thirteen trivial conserved quantities from thirteen exact conserved quantities are also received.