An upper bound for the amplitude of limit cycles of Liénard-type differential systems
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 $\{(x,y)\in\mathbb{R}^2: x<0\}$ and $\{(x,y)\in\mathbb{R}^2: x>0\}$ respectively, we provide a criterion conce...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2017-05-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5416 |
| Summary: | 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 $\{(x,y)\in\mathbb{R}^2: x<0\}$ and $\{(x,y)\in\mathbb{R}^2: x>0\}$ 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 $\{(x,y)\in\mathbb{R}^2: x<0\}$ (resp. $\{(x,y)\in\mathbb{R}^2: x>0\}$) 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. |
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| ISSN: | 1417-3875 1417-3875 |