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Bifurcations of nontwisted heteroclinic loop with resonant eigenvalues
Yinlai Jin1, Xiaowei Zhu2, Zheng Guo1
1School of Science, Linyi University, Linyi, Shandong 276005, China.
Abstract:
By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop with resonant eigenvalues. The existence, numbers, and existence regions of 1-heteroclinic loop, 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits are obtained. Meanwhile, we give the corresponding bifurcation surfaces.
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