title: Bifurcations of nontwisted heteroclinic loop with resonant eigenvalues.
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.
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Yinlai
authors.initials: Y
authors.lastname: Jin
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China ; School of Mathematics Science, Shandong Normal University, Jinan 250014, China.
authors.forename: Xiaowei
authors.initials: X
authors.lastname: Zhu
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Zheng
authors.identifier: 0000-0001-8930-1114
authors.initials: Z
authors.lastname: Guo
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Han
authors.initials: H
authors.lastname: Xu
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China ; School of Mathematics Science, Shandong Normal University, Jinan 250014, China.
authors.forename: Liqun
authors.initials: L
authors.lastname: Zhang
authors.affiliation: School of Science, Linyi University, Linyi, Shandong 276005, China ; School of Mathematics Science, Shandong Normal University, Jinan 250014, China.
authors.forename: Benyan
authors.initials: B
authors.lastname: Ding
mesh_terms: D008962:Models, Theoretical