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, issue 1

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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https://doi.org/10.1155/2013/152518

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:152518

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