Some bifurcation methods of finding limit cycles
In this paper we outline some methods of finding limit cycles for planar autonomous systems with small parameter perturbations. Three ways of studying Hopf bifurcations and the method of Melnikov functions in studying Poincaré bifurcations are introduced briefly. A new method of stability-changing i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.67 |
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| _version_ | 1832590232182063104 |
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| author | Maoan Han Tonghua Zhang |
| author_facet | Maoan Han Tonghua Zhang |
| author_sort | Maoan Han |
| collection | DOAJ |
| description | In this paper we outline some methods of finding limit cycles for planar autonomous systems with small parameter perturbations. Three ways of studying Hopf bifurcations and the method of Melnikov functions in studying Poincaré bifurcations are introduced briefly. A new method of stability-changing in studying homoclinic bifurcation is described along with some interesting applications to polynomial systems. |
| format | Article |
| id | doaj-art-017e218712304139b8b824b61396e8d7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-017e218712304139b8b824b61396e8d72025-01-24T01:51:11ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-0131677710.3934/mbe.2006.3.67Some bifurcation methods of finding limit cyclesMaoan Han0Tonghua Zhang1Department of Mathematics, Shanghai Normal University, Shanghai 200234Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240 PRIn this paper we outline some methods of finding limit cycles for planar autonomous systems with small parameter perturbations. Three ways of studying Hopf bifurcations and the method of Melnikov functions in studying Poincaré bifurcations are introduced briefly. A new method of stability-changing in studying homoclinic bifurcation is described along with some interesting applications to polynomial systems.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.67melnikov functionhomoclinic bifurcationstability-changinghopf bifurcations.poincare bifurcationslimit cyclehilbert's 16th problem |
| spellingShingle | Maoan Han Tonghua Zhang Some bifurcation methods of finding limit cycles Mathematical Biosciences and Engineering melnikov function homoclinic bifurcation stability-changing hopf bifurcations. poincare bifurcations limit cycle hilbert's 16th problem |
| title | Some bifurcation methods of finding limit cycles |
| title_full | Some bifurcation methods of finding limit cycles |
| title_fullStr | Some bifurcation methods of finding limit cycles |
| title_full_unstemmed | Some bifurcation methods of finding limit cycles |
| title_short | Some bifurcation methods of finding limit cycles |
| title_sort | some bifurcation methods of finding limit cycles |
| topic | melnikov function homoclinic bifurcation stability-changing hopf bifurcations. poincare bifurcations limit cycle hilbert's 16th problem |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.67 |
| work_keys_str_mv | AT maoanhan somebifurcationmethodsoffindinglimitcycles AT tonghuazhang somebifurcationmethodsoffindinglimitcycles |