Geodesic
An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system
Archivum mathematicum, Tome 56 (2020) no. 4, pp. 199-206 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our previous result and the result of Gasull et al. are improved partially.
In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our previous result and the result of Gasull et al. are improved partially.
DOI : 10.5817/AM2020-4-199
Classification : 34C07, 34C25, 34C26, 34D20
Keywords: Liénard system; Bogdanov-Takens system; limit cycle; Bendixson-Dulac criterion; algebraic invariant curve 
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Hayashi, Makoto. An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system. Archivum mathematicum, Tome 56 (2020) no. 4, pp. 199-206. doi: 10.5817/AM2020-4-199

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