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Limit cycles of discontinuous piecewise differential systems formed by linear centers in R2 and separated by two circles |
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| Affiliation: | 1. Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Spain;2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona 08193, Spain;3. Center for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, 1049-001, Portugal |
| Abstract: | We show that discontinuous planar piecewise differential systems formed by linear centers and separated by two concentric circles can have at most three limit cycles. Usually is a difficult problem to provide the exact upper bound that a class of differential systems can exhibit. Here we also provide examples of such systems with zero, one, two, or three limit cycles. |
| Keywords: | Limit cycles Linear centers Continuous piecewise linear differential systems Discontinuous piecewise differential systems First integrals |
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