Liénard equation and its generalizations
In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a generalization of such systems and we study their center conditions and the number of small-amplitude limit cycles that can bifurcate from the origi...
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2017 |
| Country: | España |
| Institution: | Universitat de Lleida (UdL) |
| Repository: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/62977 |
| Online Access: | https://doi.org/10.1142/S021812741750081X http://hdl.handle.net/10459.1/62977 |
| Access Level: | Open access |
| Keyword: | Center problem Analytic integrability Liénard differential systems |
| Summary: | In this paper, we first present a survey of the known results on limit cycles and center conditions for Liénard differential systems. Next we propose a generalization of such systems and we study their center conditions and the number of small-amplitude limit cycles that can bifurcate from the origin. Computing the focal values and using Gröbner bases we find the center conditions for such systems up to a certain degree. We also establish a conjecture about the center conditions for such systems when they have arbitrary degree. |
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