Address: Department of Mathematics, College of Science and Technology, Nihon University, Funabashi, Chiba, 274-8501, JAPAN
E-mail: hayashi.makoto@nihon-u.ac.jp
Abstract: 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.
AMSclassification: primary 34C07; secondary 34C25, 34C26, 34D20.
Keywords: Liénard system, Bogdanov-Takens system, limit cycle, Bendixson-Dulac criterion, algebraic invariant curve.
DOI: 10.5817/AM2020-4-199