Maximum number of limit cycles for generalized Liénard polynomial differential systems

Berbache, Aziza, Bendjeddou, Ahmed, and Benadouane, Sabah. "Maximum number of limit cycles for generalized Liénard polynomial differential systems." Mathematica Bohemica 146.2 (2021): 151-165. <http://eudml.org/doc/297992>.

@article{Berbache2021,
abstract = {We consider limit cycles of a class of polynomial differential systems of the form \[ \{\left\lbrace \begin\{array\}\{ll\} \dot\{x\}=y, \\ \dot\{y\}=-x-\varepsilon (g\_\{21\}( x) y^\{2\alpha +1\} +f\_\{21\}(x) y^\{2\beta \})-\varepsilon ^\{2\}(g\_\{22\}( x) y^\{2\alpha +1\}+f\_\{22\}( x) y^\{2\beta \}), \end\{array\}\right.\} \] where $\beta $ and $\alpha $ are positive integers, $g_\{2j\}$ and $f_\{2j\}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\varepsilon $ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot\{x\}=y$, $\dot\{y\}=-x$ using the averaging theory of first and second order.},
author = {Berbache, Aziza, Bendjeddou, Ahmed, Benadouane, Sabah},
journal = {Mathematica Bohemica},
keywords = {polynomial differential system; limit cycle; averaging theory},
language = {eng},
number = {2},
pages = {151-165},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximum number of limit cycles for generalized Liénard polynomial differential systems},
url = {http://eudml.org/doc/297992},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Berbache, Aziza
AU - Bendjeddou, Ahmed
AU - Benadouane, Sabah
TI - Maximum number of limit cycles for generalized Liénard polynomial differential systems
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 2
SP - 151
EP - 165
AB - We consider limit cycles of a class of polynomial differential systems of the form \[ {\left\lbrace \begin{array}{ll} \dot{x}=y, \\ \dot{y}=-x-\varepsilon (g_{21}( x) y^{2\alpha +1} +f_{21}(x) y^{2\beta })-\varepsilon ^{2}(g_{22}( x) y^{2\alpha +1}+f_{22}( x) y^{2\beta }), \end{array}\right.} \] where $\beta $ and $\alpha $ are positive integers, $g_{2j}$ and $f_{2j}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\varepsilon $ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot{x}=y$, $\dot{y}=-x$ using the averaging theory of first and second order.
LA - eng
KW - polynomial differential system; limit cycle; averaging theory
UR - http://eudml.org/doc/297992
ER -