Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774329 | Journal of Differential Equations | 2017 | 14 Pages |
Abstract
Symmetric Liénard system xË=yâF(x),yË=âg(x) (i.e. F(x) and g(x) are odd functions) is studied. It is well known that under some hypotheses, this system has a unique limit cycle. We develop a method to give both the upper bound and lower bound of the amplitude, which is the maximal value of the x-coordinate, of the unique limit cycle. As an application, we consider van der Pol equation xË=yâμ(x3/3âx),yË=âx, where μ>0. Denote by A(μ) the amplitude of its unique limit cycle, then for any μ, we show that A(μ)<2.0976 and for μ=1,2, we show that A(μ)>2. Both the upper bound and the lower bound improve the existing ones.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yuli Cao, Changjian Liu,