Bifurcation of limit cycles from a heteroclinic loop with two cusps |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. Department of Mathematics, Swinburne University of Technology, Victoria 3122, Australia;1. MAPMO–UMR 6628, Département de mathématiques, Université d''Orléans, 45067 Orléans cedex 2, France;2. Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Binh Dinh, Vietnam;1. School of Mathematical Science, East China Normal University, Shanghai, 200241, China;2. School of Mathematical Science, Harbin Engineering University, Harbin, 15001, China;1. Faculty of Engineering, Cairo University, Giza, Egypt;2. Faculty of Information Engineering and Technology (IET), German University in Cairo (GUC), Cairo, Egypt;3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt;1. Departmento de Matemática, Universidade de Brasília, 70910-900 Brasilia, Brazil |
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| Abstract: | In this paper, we study the expansion of the first Melnikov function for general near-Hamiltonian systems near a heteroclinic loop with two cusps of order 1 or 2, obtain the formulas for the first coefficients appearing in the expansion, and establish some bifurcation theorems on the number of limit cycles. We also give some application examples. |
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