Codimension 2 reversible heteroclinic bifurcations with inclination flips |
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Authors: | YanCong Xu DeMing Zhu GuiFeng Deng |
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Institution: | (1) Department of Mathematics, Hangzhou Normal University, Hangzhou (Xiasha), 310036, China;(2) Department of Mathematics, East China Normal University, Shanghai, 200241, China;(3) School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai, 201620, China |
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Abstract: | In this paper, the heteroclinic bifurcation problem with real eigenvalues and two inclination-flips is investigated in a four-dimensional
reversible system. We perform a detailed study of this case by using the method originally established in the papers “Problems
in Homoclinic Bifurcation with Higher Dimensions” and “Bifurcation of Heteroclinic Loops,” and obtain fruitful results, such
as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops, R-symmetric homoclinic orbit and R-symmetric periodic orbit. The double R-symmetric homoclinic bifurcation (i.e., two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found, and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated. The relevant bifurcation surfaces and the
existence regions are also located.
This work was supported by National Natural Science Foundation of China (Grant No. 10671069) |
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Keywords: | heteroclinic bifurcation inclination flips reversible system |
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