TY - JOUR
T1 - Non-existence, existence, and uniqueness of limit cycles for a generalization of the Van der Pol–Duffing and the Rayleigh–Duffing oscillators
AU - Cândido, Murilo R.
AU - Llibre, Jaume
AU - Valls, Claudia
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/6
Y1 - 2020/6
N2 - We study the limit cycles of some cubic family of differential equations, containing the well-known Van der Pol–Duffing and Rayleigh–Duffing oscillators. In particular, we characterize for the class of differential systems here studied the non-existence, existence and uniqueness of limit cycles. Moreover we provide their global phase portraits in the Poincaré disk.
AB - We study the limit cycles of some cubic family of differential equations, containing the well-known Van der Pol–Duffing and Rayleigh–Duffing oscillators. In particular, we characterize for the class of differential systems here studied the non-existence, existence and uniqueness of limit cycles. Moreover we provide their global phase portraits in the Poincaré disk.
KW - Limit cycles
KW - Rayleigh–Duffing oscillator
KW - Van der Pol–Duffing oscillator
UR - https://www.scopus.com/pages/publications/85081992750
U2 - 10.1016/j.physd.2020.132458
DO - 10.1016/j.physd.2020.132458
M3 - Article
AN - SCOPUS:85081992750
SN - 0167-2789
VL - 407
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 132458
ER -