TY - JOUR
T1 - Limit cycles of a generalised Mathieu differential system
AU - Diab, Zouhair
AU - Guirao, Juan L.G.
AU - Llibre, Jaume
AU - Makhlouf, Amar
N1 - Publisher Copyright:
© 2021 Zouhair Diab et al., published by Sciendo 2021.
PY - 2021
Y1 - 2021
N2 - We study the maximum number of limit cycles which bifurcate from the periodic orbits of the linear centre x=y, y=-x, when it is perturbed in the form [equcation presented], where ϵ > 0 is a small parameter, l and m are positive integers, P(x, y) and Q(x, y) are arbitrary polynomials of degree n, and θ = arctan (y/x). As we shall see the differential system (1) is a generalisation of the Mathieu differential equation. The tool for studying such limit cycles is the averaging theory.
AB - We study the maximum number of limit cycles which bifurcate from the periodic orbits of the linear centre x=y, y=-x, when it is perturbed in the form [equcation presented], where ϵ > 0 is a small parameter, l and m are positive integers, P(x, y) and Q(x, y) are arbitrary polynomials of degree n, and θ = arctan (y/x). As we shall see the differential system (1) is a generalisation of the Mathieu differential equation. The tool for studying such limit cycles is the averaging theory.
KW - averaging theory
KW - differential system
KW - Limit cycle
UR - https://www.scopus.com/pages/publications/85137396682
U2 - 10.2478/amns.2021.2.00180
DO - 10.2478/amns.2021.2.00180
M3 - Article
AN - SCOPUS:85137396682
SN - 2444-8656
JO - Applied Mathematics and Nonlinear Sciences
JF - Applied Mathematics and Nonlinear Sciences
ER -