Artículo
Limit cycles from a monodromic infinity in planar piecewise linear systems
Autor/es | Freire Macías, Emilio
Ponce Núñez, Enrique Torregrosa, Joan Torres Peral, Francisco |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2021-04-15 |
Fecha de depósito | 2021-01-15 |
Publicado en |
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Resumen | Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with ... Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is obtained. Instead of the usual Bendixson transformation to work near infinity, a more direct approach is introduced by taking suitable coordinates for the crossing points of the possible periodic orbits with the separation straight line. The required computations to characterize the stability and bifurcations of the periodic orbit at infinity are much easier. It is shown that the Hopf bifurcation at infinity can have degeneracies of co-dimension three and, in particular, up to three limit cycles can bifurcate from the periodic orbit at infinity. This provides a new mechanism to explain the claimed maximum number of limit cycles in this family of systems. The centers at infinity classification together with the limit cycles bifurcating from them are also analyzed |
Identificador del proyecto | P12-FQM-1658
2017 SGR 1617 MTM2016-77278-P MTM2017-87915-D2-1-P PGC2018-096265-B-I00 PID2019-104658GB-I00 H2020-MSCA-RISE-2017-777911 |
Cita | Freire Macías, E., Ponce Núñez, E., Torregrosa, J. y Torres Peral, F. (2021). Limit cycles from a monodromic infinity in planar piecewise linear systems. Journal of Mathematical Analysis and Applications, 496 (2), Article 124818. |
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