Degenerate bifurcations of nontwisted heterodimensional cycles with codimension 3 |
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Authors: | Dan Liu Fengjie GengDeming Zhu |
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Affiliation: | Department of Mathematics, East China Normal University, Shanghai 200062, China |
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Abstract: | Bifurcations of heterodimensional cycles with highly degenerate conditions are studied by establishing a suitable local coordinate system in three-dimensional vector fields. The existence, coexistence and noncoexistence of the periodic orbit, homoclinic loop, heteroclinic loop and double periodic orbit are obtained under some generic hypotheses. The bifurcation surfaces and the existence regions are located; the number of the bifurcation surfaces exhibits variety and complexity of the bifurcation of degenerate heterodimensional cycles. The corresponding bifurcation graph is also drawn. |
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Keywords: | Heterodimensional cycle Local coordinates Successor functions Bifurcation surface Homoclinic loop Periodic orbit Double periodic orbit |
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