TY - JOUR
T1 - Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line
AU - Bastos, Jefferson L. R.
AU - Buzzi, Claudio A.
AU - Torregrosa, Joan
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/6/19
Y1 - 2023/6/19
N2 - In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type
AB - In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. In this class and considering a degenerated Hopf bifurcation near families of centers we obtain again at least five limit cycles but now from infinity, which is of monodromic type, and with simpler computations. The proof uses a partial classification of the center problem when both systems are of center type
KW - Piecewise linear planar vector fields
KW - Local cyclicity
KW - Nonsmooth boundary
KW - Center-focus problem
UR - http://www.scopus.com/inward/record.url?scp=85162873199&partnerID=8YFLogxK
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=9031882
UR - https://www.mendeley.com/catalogue/8ed2c515-e104-3004-93a3-fd9cde535d4e/
U2 - 10.1007/s12346-023-00817-9
DO - 10.1007/s12346-023-00817-9
M3 - Article
SN - 1575-5460
VL - 22
JO - Qualitative Theory of Dynamical Systems
JF - Qualitative Theory of Dynamical Systems
IS - 4
M1 - 125
ER -