A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems

被引：7
|
作者：
Leonov, G. A. [1 ]
Kuznetsov, N. V. [1 ]
Kudryashova, E. V. [1 ]
机构：
[1] St Petersburg State Univ, St Petersburg 199034, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2011年 / 272卷
关键词：
Lyapunov quantities; limit cycle; symbolic computations; LIMIT-CYCLES;
D O I：
10.1134/S008154381102009X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A direct method is proposed for studying the behavior of two-dimensional dynamical systems in the critical case when the linear part of the system has two purely imaginary eigenvalues. This method allows one to construct approximations to solutions of the system and to the "turn-round" time of the trajectory in the form of a finite series in powers of the initial datum. With the help of symbolic computations and the proposed method, first approximations of a solution are constructed and expressions for the first three Lyapunov quantities of the Li,nard system are written.
引用
收藏
页码：119 / 126
页数：8
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