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Bifurcations of Double Homoclinic Loops with Inclination Flip and Nonresonant Eigenvalues
  
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KeyWord:Double homoclinic loops; Nonresonant eigenvalues; Inclination flip; Periodic orbit; Bifurcation.
Author NameAffiliation
Qianqian Jia School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China 
Weipeng Zhang School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China 
Qiuying Lu School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China 
Xiaodong Li School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China 
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Abstract:
      In this work, bifurcation analysis near double homoclinic loops with Ws inclination flip of Γ1 and nonresonant eigenvalues is presented in a four-dimensional system. We establish a Poincar´e map by constructing local active coordinates approach in some tubular neighborhood of unperturbed double homoclinic loops. Through studying the bifurcation equations, we obtain the condition that the original double homoclinic loops are persistent, and get the existence or the nonexistence regions of the large 1-homoclinic orbit and the large 1-periodic orbit. At last, an analytical example is given to illustrate our main results.