Geodesic
On the limit cycle of the Liénard equation
Archivum mathematicum, Tome 36 (2000) no. 1, pp. 25-31

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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 $\rho (\mu )2.5425$.
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 $\rho (\mu )2.5425$.
Classification : 34C05
Keywords: van der Pol equation; limit cycle; amplitude 
Odani, Kenzi. On the limit cycle of the Liénard equation. Archivum mathematicum, Tome 36 (2000) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/ARM_2000_36_1_a3/
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_1_a3/}
}
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