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An upper bound for the amplitude of limit cycles of Liénard-type differential systems
- Source :
- Electronic Journal of Qualitative Theory of Differential Equations, Vol 2017, Iss 34, Pp 1-14 (2017)
- Publication Year :
- 2017
- Publisher :
- University of Szeged, 2017.
-
Abstract
- In this paper, we investigate the position problem of limit cycles for a class of Liénard-type differential systems. By considering the upper bound of the amplitude of limit cycles on $\{(x,y)\in\mathbb{R}^2: x0\}$ respectively, we provide a criterion concerning an explicit upper bound for the amplitude of the unique limit cycle of the Liénard-type system on the plane. Here the amplitude of a limit cycle on $\{(x,y)\in\mathbb{R}^2: x0\}$) is defined as the minimum (resp. maximum) value of the $x$-coordinate on such a limit cycle. Finally, we give two examples including an application to predator-prey system model to illustrate the obtained theoretical result, and Matlab simulations are presented to show the agreement between our theoretical result with the simulation analysis.
- Subjects :
- liénard-type system
limit cycle
amplitude
upper bound
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 14173875
- Volume :
- 2017
- Issue :
- 34
- Database :
- Directory of Open Access Journals
- Journal :
- Electronic Journal of Qualitative Theory of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.8d2cb2f1826d4f0da3aed3e16045a15a
- Document Type :
- article
- Full Text :
- https://doi.org/10.14232/ejqtde.2017.1.34