The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues
The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/152518 |
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| _version_ | 1849410107560951808 |
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| author | Xiaodong Li Weipeng Zhang Fengjie Geng Jicai Huang |
| author_facet | Xiaodong Li Weipeng Zhang Fengjie Geng Jicai Huang |
| author_sort | Xiaodong Li |
| collection | DOAJ |
| description | The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system. |
| format | Article |
| id | doaj-art-802d63c77e1f4181be5518b2480ca9af |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-802d63c77e1f4181be5518b2480ca9af2025-08-20T03:35:15ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/152518152518The Twisting Bifurcations of Double Homoclinic Loops with Resonant EigenvaluesXiaodong Li0Weipeng Zhang1Fengjie Geng2Jicai Huang3School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, ChinaSchool of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, ChinaSchool of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, ChinaThe twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system.http://dx.doi.org/10.1155/2013/152518 |
| spellingShingle | Xiaodong Li Weipeng Zhang Fengjie Geng Jicai Huang The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues Abstract and Applied Analysis |
| title | The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues |
| title_full | The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues |
| title_fullStr | The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues |
| title_full_unstemmed | The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues |
| title_short | The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues |
| title_sort | twisting bifurcations of double homoclinic loops with resonant eigenvalues |
| url | http://dx.doi.org/10.1155/2013/152518 |
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