On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 818-823
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We consider the class of polynomial differential systems of the form $\dot{x} =\,\lambda x\,-\,y\,+\,{{P}_{n}}\left( x,\,y \right)$ , $\dot{y} =\,x\,+\,\lambda y\,+\,{{Q}_{n}}\left( x,\,y \right)$ where ${{P}_{n}}$ and ${{Q}_{n}}$ are homogeneous polynomials of degree $n$ . For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.
Mots-clés :
34C35, 34D30, polynomial differential system, limit cycles, differential equations on the cylinder
Llibre, Jaume; Zhang, Xiang. On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 818-823. doi: 10.4153/CMB-2015-062-1
@article{10_4153_CMB_2015_062_1,
author = {Llibre, Jaume and Zhang, Xiang},
title = {On the {Limit} {Cycles} of {Linear} {Differential} {Systems} with {Homogeneous} {Nonlinearities}},
journal = {Canadian mathematical bulletin},
pages = {818--823},
year = {2015},
volume = {58},
number = {4},
doi = {10.4153/CMB-2015-062-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-062-1/}
}
TY - JOUR AU - Llibre, Jaume AU - Zhang, Xiang TI - On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities JO - Canadian mathematical bulletin PY - 2015 SP - 818 EP - 823 VL - 58 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-062-1/ DO - 10.4153/CMB-2015-062-1 ID - 10_4153_CMB_2015_062_1 ER -
%0 Journal Article %A Llibre, Jaume %A Zhang, Xiang %T On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities %J Canadian mathematical bulletin %D 2015 %P 818-823 %V 58 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-062-1/ %R 10.4153/CMB-2015-062-1 %F 10_4153_CMB_2015_062_1
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