Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip and an inclination flip. When the nonhyperbolic...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/585609 |
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| _version_ | 1832550228350205952 |
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| author | Fengjie Geng Junfang Zhao |
| author_facet | Fengjie Geng Junfang Zhao |
| author_sort | Fengjie Geng |
| collection | DOAJ |
| description | The bifurcations of
heteroclinic loop with one nonhyperbolic equilibrium and one
hyperbolic saddle are considered, where the nonhyperbolic
equilibrium is supposed to undergo a transcritical bifurcation;
moreover, the heteroclinic loop has an orbit flip and an inclination
flip. When the nonhyperbolic equilibrium does not undergo a
transcritical bifurcation, we establish the coexistence and
noncoexistence of the periodic orbits and homoclinic orbits. While
the nonhyperbolic equilibrium undergoes the transcritical
bifurcation, we obtain the noncoexistence of the periodic orbits and
homoclinic orbits and the existence of two or three heteroclinic
orbits. |
| format | Article |
| id | doaj-art-94286d7020bd4b6995fb5953fff23a6a |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-94286d7020bd4b6995fb5953fff23a6a2025-02-03T06:07:20ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/585609585609Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic EquilibriaFengjie Geng0Junfang Zhao1School of Science, China University of Geosciences (Beijing), Beijing, 100083, ChinaSchool of Science, China University of Geosciences (Beijing), Beijing, 100083, ChinaThe bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip and an inclination flip. When the nonhyperbolic equilibrium does not undergo a transcritical bifurcation, we establish the coexistence and noncoexistence of the periodic orbits and homoclinic orbits. While the nonhyperbolic equilibrium undergoes the transcritical bifurcation, we obtain the noncoexistence of the periodic orbits and homoclinic orbits and the existence of two or three heteroclinic orbits.http://dx.doi.org/10.1155/2014/585609 |
| spellingShingle | Fengjie Geng Junfang Zhao Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria The Scientific World Journal |
| title | Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria |
| title_full | Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria |
| title_fullStr | Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria |
| title_full_unstemmed | Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria |
| title_short | Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria |
| title_sort | bifurcations of orbit and inclination flips heteroclinic loop with nonhyperbolic equilibria |
| url | http://dx.doi.org/10.1155/2014/585609 |
| work_keys_str_mv | AT fengjiegeng bifurcationsoforbitandinclinationflipsheteroclinicloopwithnonhyperbolicequilibria AT junfangzhao bifurcationsoforbitandinclinationflipsheteroclinicloopwithnonhyperbolicequilibria |