On the limit cycle of the Liénard equation
Odani, Kenzi
Archivum Mathematicum, Tome 036 (2000), p. 25-31 / Harvested from Czech Digital Mathematics Library
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In the paper, we give an existence theorem of periodic solution for Liénard equation $\dot{x}=y-F(x)$, $\dot{y}=-g(x)$. As a result, we estimate the amplitude $\rho (\mu )$ (maximal $x$-value) of the limit cycle of the van der Pol equation $\dot{x}=y-\mu (x^3/3-x)$, $\dot{y}=-x$ from above by $\rho (\mu )<2.3439$ for every $\mu \ne 0$. The result is an improvement of the author’s previous estimation $\rho (\mu )<2.5425$.

Publié le : 2000-01-01
Classification:  34C05 
@article{107715,
     author = {Kenzi Odani},
     title = {On the limit cycle of the Li\'enard equation},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {25-31},
     zbl = {1048.34067},
     mrnumber = {1751611},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107715}
}

Odani, Kenzi. On the limit cycle of the Liénard equation. Archivum Mathematicum, Tome 036 (2000) pp. 25-31. http://gdmltest.u-ga.fr/item/107715/

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