title: Bifurcations and stability of nondegenerated homoclinic loops for higher dimensional systems.
abstract: By using the foundational solutions of the linear variational equation of the unperturbed system along the homoclinic orbit as the local current coordinates system of the system in the small neighborhood of the homoclinic orbit, we discuss the bifurcation problems of nondegenerated homoclinic loops. Under the nonresonant condition, existence, uniqueness, and incoexistence of 1-homoclinic loop and 1-periodic orbit, the inexistence of k-homoclinic loop and k-periodic orbit is obtained. Under the resonant condition, we study the existence of 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits; the coexistence of 1-homoclinic loop and 1-periodic orbit. Moreover, we give the corresponding existence fields and bifurcation surfaces. At last, we study the stability of the homoclinic loop for the two cases of non-resonant and resonant, and we obtain the corresponding criterions.
authors.affiliation: Science College, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Yinlai
authors.initials: Y
authors.lastname: Jin
authors.affiliation: Science College, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Feng
authors.initials: F
authors.lastname: Li
authors.affiliation: Science College, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Han
authors.initials: H
authors.lastname: Xu
authors.affiliation: Science College, Linyi University, Linyi, Shandong 276005, China.
authors.forename: Jing
authors.initials: J
authors.lastname: Li
authors.affiliation: Science College, 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: Science College, 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: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology; D003198:Computer Simulation; D003199:Computer Systems; D006801:Humans; D016014:Linear Models; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D011159:Population Surveillance; D012984:Software