TY - JOUR
T1 - Dynamics of the polynomial differential systems with homogeneous nonlinearities and a star node
AU - Bendjeddou, Ahmed
AU - Llibre, Jaume
AU - Salhi, Tayeb
PY - 2013/4/15
Y1 - 2013/4/15
N2 - We consider the class of polynomial differential equations x=λx+Pn(x,y), y=λy+Qn(x,y), in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n>1 and λ≠0, i.e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin.We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin. © 2013 .
AB - We consider the class of polynomial differential equations x=λx+Pn(x,y), y=λy+Qn(x,y), in R2 where Pn(x, y) and Qn(x, y) are homogeneous polynomials of degree n>1 and λ≠0, i.e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin.We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin. © 2013 .
KW - Cubic system
KW - Limit cycle
KW - Star node
UR - https://www.scopus.com/pages/publications/84874250065
U2 - 10.1016/j.jde.2013.01.032
DO - 10.1016/j.jde.2013.01.032
M3 - Article
SN - 0022-0396
VL - 254
SP - 3530
EP - 3537
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 8
ER -