BIFURCATION OF ROUGH HETEROCLINIC LOOP WITH ORBIT FLIPS
2012 ◽
Vol 22
(11)
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pp. 1250278
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Keyword(s):
In this paper, heteroclinic loop bifurcations with double orbit flips are investigated in four-dimensional vector fields. We obtain the bifurcation equations by setting up a local coordinate system near the rough heteroclinic orbit and establishing the Poincaré map. By means of the bifurcation equations, we investigate the existence, coexistence and noncoexistence of periodic orbit, homoclinic loop and heteroclinic loop under some nongeneric conditions. The approximate expressions of corresponding bifurcation curves (or surfaces) are also given. An example of application is also given to demonstrate the existence of the heteroclinic loop with double orbit flips.
2011 ◽
Vol 21
(01)
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pp. 255-273
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2008 ◽
Vol 18
(04)
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pp. 1069-1083
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2020 ◽
Vol 30
(16)
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pp. 2050246
2010 ◽
Vol 20
(02)
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pp. 491-508
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Keyword(s):
1993 ◽
Vol 44
(3)
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pp. 510-536
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Keyword(s):
2003 ◽
Vol 13
(03)
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pp. 553-570
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2013 ◽
Vol 23
(05)
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pp. 1350080
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Keyword(s):
2017 ◽
Vol 27
(08)
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pp. 1750120