The Twisting Bifurcations of Double Homoclinic Loops with Resonant Eigenvalues

Xiaodong Li, Weipeng Zhang, Fengjie Geng and Jicai Huang

Abstract and Applied Analysis, 2013, vol. 2013, 1-11

Abstract:

The twisting bifurcations of double homoclinic loops with resonant eigenvalues are investigated in four-dimensional systems. The coexistence or noncoexistence of large 1-homoclinic orbit and large 1-periodic orbit near double homoclinic loops is given. The existence or nonexistence of saddle-node bifurcation surfaces is obtained. Finally, the complete bifurcation diagrams and bifurcation curves are also given under different cases. Moreover, the methods adopted in this paper can be extended to a higher dimensional system.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:152518

DOI: 10.1155/2013/152518

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