TY - JOUR
T1 - Limit Cycles of the Generalized Polynomial Liénard Differential Systems
AU - Boulfoul , Amel
AU - Makhlouf , Amar
JO - Annals of Applied Mathematics
VL - 3
SP - 221
EP - 233
PY - 2022
DA - 2022/06
SN - 32
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20639.html
KW - limit cycle, periodic orbit, Liénard differential system, averaging theory.
AB - <p style="text-align: justify;">Using the averaging theory of first and second order we study the maximum
number of limit cycles of generalized Liénard differential systems $$\begin{cases} \dot{x}= y + ϵh^1_l
(x) + ϵ^2h^2_l
(x),&nbsp; \\ \dot{y}= −x − ϵ(f^1_n
(x)y^{2p+1}+ g^1_m(x)) + ϵ^2
(f^2_n(x)y^{2p+1}+ g^2_m(x)), \end{cases}$$ which bifurcate from the periodic orbits of the linear center $\dot{x} = y,$ $\dot{y}= −x,$ where $ϵ$ is a small parameter. The polynomials $h^1_l$ and $h^2_l$ have degree $l;$ $f^1_n$ and $f^2_n$ have degree $n;$ and $g^1_m,$ $g^2_m$ have degree $m.$ $p ∈ \mathbb{N}$ and [·] denotes the
integer part function.</p>