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On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities

Published online by Cambridge University Press:  20 November 2018

Jaume Llibre  and
Xiang Zhang
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain e-mail: jllibre@mat.uab.cat
Xiang Zhang
Affiliation:
Department of Mathematics, MOE–LSC, Shanghai Jiao tong University, Shanghai, 200240, P. R. China e-mail: xzhang@sjtu.edu.cn
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Abstract

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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.

Keywords

34C3534D30polynomial differential systemlimit cyclesdifferential equations on the cylinder
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 4 , 01 December 2015 , pp. 818 - 823
Copyright
Copyright © Canadian Mathematical Society 2015

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