Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian
In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at le...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi-Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5813596 |
| Summary: | In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at least 3 limit cycles emerging from the period annulus, and 3 limit cycles are near the boundaries. |
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| ISSN: | 1076-2787 1099-0526 |