On the limit cycle of the Liénard equation
Archivum Mathematicum (2000)
- Volume: 036, Issue: 1, page 25-31
- ISSN: 0044-8753
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topOdani, Kenzi. "On the limit cycle of the Liénard equation." Archivum Mathematicum 036.1 (2000): 25-31. <http://eudml.org/doc/248523>.
@article{Odani2000,
abstract = {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 $\rho (\mu )<2.5425$.},
author = {Odani, Kenzi},
journal = {Archivum Mathematicum},
keywords = {van der Pol equation; limit cycle; amplitude; van der Pol equation; limit cycle; amplitude},
language = {eng},
number = {1},
pages = {25-31},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the limit cycle of the Liénard equation},
url = {http://eudml.org/doc/248523},
volume = {036},
year = {2000},
}
TY - JOUR
AU - Odani, Kenzi
TI - On the limit cycle of the Liénard equation
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 1
SP - 25
EP - 31
AB - 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 $\rho (\mu )<2.5425$.
LA - eng
KW - van der Pol equation; limit cycle; amplitude; van der Pol equation; limit cycle; amplitude
UR - http://eudml.org/doc/248523
ER -
References
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