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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2356-6140 1537-744X |