Bifurcation of limit cycles by perturbing piecewise non-Hamiltonian systems with nonlinear switching manifold |
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| Affiliation: | 1. Universidade Estadual Paulista, IBILCE-UNESP, Av. Cristovão Colombo, 2265, 15.054-000, S. J. Rio Preto, SP, Brazil;2. Universitat Autònoma de Barcelona, UAB, Edifici C Facultat de Ciències, 08193 Bellaterra, Barcelona, Spain;3. Universidade Estadual de Campinas, IMECC-UNICAMP, R. Sérgio Buarque de Holanda, 651, 13.083-859, Campinas, SP, Brazil;1. Instituto de Matemática e Estatística, Universidade Federal de Goiás Campus II, Samambaia, 74001-970, Goiânia, GO, Brazil;2. Departamento de Matemática, Universidade Federal de Viçosa, Campus Universitário, 36570-000, Viçosa, MG, Brazil;3. Departamento de Matemática, Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz, 13083-859, Campinas, SP, Brazil;1. Department of Mathematics, Lingnan Normal University, Zhanjiang, Guangdong 524008, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;3. Department of Mathematics, Shandong University of Science and Technology, Qingdao, Shandong 266590, China |
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| Abstract: | This paper is devoted to the study of limit cycles that can bifurcate of a perturbation of piecewise non-Hamiltonian systems with nonlinear switching manifold. We derive the first order Melnikov function to these systems. As application, the sharp upper bound of the number of bifurcated limit cycles of two concrete systems, whose switching manifolds are algebraic curves, is presented. |
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| Keywords: | Piecewise non-Hamiltonian systems Limit cycle Melnikov function |
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