On the uniqueness of limit cycle for certain Liénard systems without symmetry
The problem of the uniqueness of limit cycles for Liénard systems is investigated in connection with the properties of the function F(x). When α and β (α < 0 < β) are the unique nontrivial solutions of the equation F(x) = 0, necessary and sufficient conditions in order that all the possible li...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Matematikai modell, Liénard rendszer, Invariáns, Matematika |
| doi: | 10.14232/ejqtde.2018.1.55 |
| Online Access: | http://acta.bibl.u-szeged.hu/58130 |
| Tartalmi kivonat: | The problem of the uniqueness of limit cycles for Liénard systems is investigated in connection with the properties of the function F(x). When α and β (α < 0 < β) are the unique nontrivial solutions of the equation F(x) = 0, necessary and sufficient conditions in order that all the possible limit cycles of the system intersect the lines x = α and x = β are given. Therefore, in view of classical results, the limit cycle is unique. Some examples are presented to show the applicability of our results in situations with lack of symmetry. |
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| Terjedelem/Fizikai jellemzők: | 1-10 |
| ISSN: | 1417-3875 |