Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems |
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Authors: | Liping Li Lihong Huang |
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Affiliation: | 1. Department of Mathematics, Huzhou Teacher?s College, Huzhou, Zhejiang, 313000, PR China;2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, PR China;3. Hunan Women?s University, Changsha, Hunan, 410004, PR China |
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Abstract: | This paper investigates both homoclinic bifurcation and Hopf bifurcation which occur concurrently in a class of planar perturbed discontinuous systems of Filippov type. Firstly, based on a geometrical interpretation and a new analysis of the so-called successive function, sufficient conditions are proposed for the existence and stability of homoclinic orbit of unperturbed systems. Then, with the discussion about Poincaré map, bifurcation analyses of homoclinic orbit and parabolic–parabolic (PP) type pseudo-focus are presented. It is shown that two limit cycles can appear from the two different kinds of bifurcation in planar Filippov systems. |
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Keywords: | Planar Filippov systems Homoclinic bifurcation Hopf bifurcation Limit cycle |
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