On the limit cycles of perturbed discontinuous planar systems with 4 switching lines |
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| Affiliation: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China;2. School of Mathematics & Physics, Changzhou University, Changzhou 213164, Jiangsu, PR China;3. Department of Applied Mathematics, University of Craiova, 13 A.I. Cuza, 200585 Craiova, Romania;1. Institute of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, PR China;2. Institute of Mathematics and Statistics, Baise University, Baise, Guangxi 533000, PR China;1. Department of Medical Acupuncture and Rehabilitation, State University of Ecatepec Valley, Ecatepec State of Mexico, Av. Central s/n, Esq. Leona Vicario, Col. Valle de Anáhuac, Secc. "A", C.P. 55210 Ecatepec Estado de México, Méxicon;2. Center for Research in Mathematics, Hidalgo State Autonomous University, Carretera Pachuca-Tulancingo Km. 4.5 Col. Carboneras, C. P. 42184 Mineral de la Reforma, Hgo., México;3. Superior Studies Faculty, FES Iztacala, UNAM, México;4. Department of Physiology, Biophysics and Neuroscience, Center for Research and Advanced Studies, National Polytechnic Institute, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, AP. 14-740, México D.F. CP 07000, Méxicon |
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| Abstract: | Limit cycle bifurcations for a class of perturbed planar piecewise smooth systems with 4 switching lines are investigated. The expressions of the first order Melnikov function are established when the unperturbed system has a compound global center, a compound homoclinic loop, a compound 2-polycycle, a compound 3-polycycle or a compound 4-polycycle, respectively. Using Melnikov’s method, we obtain lower bounds of the maximal number of limit cycles for the above five different cases. Further, we derive upper bounds of the number of limit cycles for the later four different cases. Finally, we give a numerical example to verify the theory results. |
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