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- W2555276209 abstract "Symmetric Liénard system x˙=y−F(x),y˙=−g(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 x˙=y−μ(x3/3−x),y˙=−x, 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." @default.
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- W2555276209 date "2017-02-01" @default.
- W2555276209 modified "2023-09-26" @default.
- W2555276209 title "The estimate of the amplitude of limit cycles of symmetric Liénard systems" @default.
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- W2555276209 doi "https://doi.org/10.1016/j.jde.2016.10.034" @default.
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