TY - JOUR
T1 - Limit cycles of piecewise differential equations on the cylinder
AU - Bakhshalizadeh, Ali
AU - Llibre, Jaume
N1 - Publisher Copyright:
© 2021 Elsevier Masson SAS
PY - 2021/9
Y1 - 2021/9
N2 - We consider the discontinuous piecewise differential equations of the form [Formula presented] where a0(t),a1(t),…,an(t) and b0(t),b1(t),…,bm(t) are 2π-periodic functions in the variable t, and we study the number of limit cycles of such equations on the cylinder. In this way we give exact bounds for the maximum number of limit cycles that the piecewise differential equations have in function of n and m. Note that usually the discontinuous piecewise differential systems are discontinuous in the dependent variable, here the system is discontinuous in the independent variable.
AB - We consider the discontinuous piecewise differential equations of the form [Formula presented] where a0(t),a1(t),…,an(t) and b0(t),b1(t),…,bm(t) are 2π-periodic functions in the variable t, and we study the number of limit cycles of such equations on the cylinder. In this way we give exact bounds for the maximum number of limit cycles that the piecewise differential equations have in function of n and m. Note that usually the discontinuous piecewise differential systems are discontinuous in the dependent variable, here the system is discontinuous in the independent variable.
KW - Differential equations on the cylinder
KW - Hilbert number
KW - Limit cycles
KW - Piecewise smooth system
UR - http://www.scopus.com/inward/record.url?scp=85107687394&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2021.103013
DO - 10.1016/j.bulsci.2021.103013
M3 - Article
AN - SCOPUS:85107687394
SN - 0007-4497
VL - 170
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
M1 - 103013
ER -