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| Homoclinic Flip Bifurcations Accompanied by Transcritical Bifurcation |
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Citation： |
Xingbo LIU.Homoclinic Flip Bifurcations Accompanied by Transcritical Bifurcation[J].Chinese Annals of Mathematics B,2011,32(6):905~916 |
| Page view： 1803
Net amount： 1664 |
Authors： |
Xingbo LIU; |
Foundation： |
the National Natural Science Foundation of China (No. 10801051) and the Shanghai
Leading Academic Discipline Project (No. B407). |
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| Abstract： |
The bifurcations of orbit
ip homoclinic loop with nonhyperbolic equilibria are
investigated. By constructing local coordinate systems near the unperturbed homoclinic
orbit, Poincar e maps for the new system are established. Then the existence of homoclin-
ic orbit and the periodic orbit is studied for the system accompanied with transcritical
bifurcation. |
Keywords： |
Transcritical bifurcation, Homoclinic orbit, Periodic orbit, Local
coordinate system, Poincar e maps |
Classification： |
34C23, 34C37, 37C29 |
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