Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp |
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| Affiliation: | 1. Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse, France;2. Institute of Mathematics, Bulgarian Academy of Sciences, Bl. 8, 1113 Sofia, Bulgaria;1. School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276005, PR China;2. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410065, PR China;3. Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada;1. Department of Applied Mathematics, Western University, London, Ontario N6A 5B7, Canada;2. School of Science, Linyi University, Linyi, Shandong 276005, PR China;1. Institute of Mathematics, Bulgarian Academy of Sciences, Bl. 8, 1113 Sofia, Bulgaria;2. School of Mathematical Sciences, Peking University, Beijing 100871, PR China;3. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, PR China |
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| Abstract: | For a piecewise analytical Hamiltonian system with a cusp on a switch line, which has a family of periodic orbits near a generalized homoclinic loop, we study the maximum number of limit cycles bifurcating from the periodic orbits. For doing so, we first obtain the asymptotic expressions of the Melnikov functions near the loop. Finally we present two examples illustrating applications of the main results. |
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| Keywords: | Melnikov function Limit cycle Generalized homoclinic loop Cusp Piecewise smooth system |
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