TY - JOUR
T1 - Limit cycles for a class of three-dimensional polynomial differential systems
AU - Llibre, Jaume
AU - Yu, Jiang
PY - 2007/10/1
Y1 - 2007/10/1
N2 - Perturbing the system ẋ= - y(1 + x) ẏ = x(1 + x), ż = 0 inside the family of polynomial differential systems of degree n in ℝ 3, we obtain at most n 2 limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n 2 limit cycles. © Springer Science+Business Media, LLC 2007.
AB - Perturbing the system ẋ= - y(1 + x) ẏ = x(1 + x), ż = 0 inside the family of polynomial differential systems of degree n in ℝ 3, we obtain at most n 2 limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n 2 limit cycles. © Springer Science+Business Media, LLC 2007.
KW - Averaging theory
KW - Limit cycle
KW - Linear center
KW - Polynomial differential system
U2 - 10.1007/s10883-007-9025-5
DO - 10.1007/s10883-007-9025-5
M3 - Article
SN - 1079-2724
VL - 13
SP - 531
EP - 539
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 4
ER -