Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems |
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Authors: | Feng Liang Maoan Han |
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Affiliation: | 1. The Institute of Mathematics, Shanghai Normal University, Shanghai 200234, PR China;2. The Institute of Mathematics, Anhui Normal University, Wuhu 241000, PR China |
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Abstract: | In this paper, we study the bifurcation of limit cycles in piecewise smooth systems by perturbing a piecewise Hamiltonian system with a generalized homoclinic or generalized double homoclinic loop. We first obtain the form of the expansion of the first Melnikov function. Then by using the first coefficients in the expansion, we give some new results on the number of limit cycles bifurcated from a periodic annulus near the generalized (double) homoclinic loop. As applications, we study the number of limit cycles of a piecewise near-Hamiltonian systems with a generalized homoclinic loop and a central symmetric piecewise smooth system with a generalized double homoclinic loop. |
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