On the limit cycles of linear differential systems with homogeneous nonlinearities

Jaume Llibre; Xiang Zhang

doi:https://doi.org/10.4153/CMB-2015-062-1

On the limit cycles of linear differential systems with homogeneous nonlinearities

Jaume Llibre, Xiang Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© Canadian Mathematical Society 2015. We consider the class of polynomial diòerential systems of the form x = λx-y+Pn(x, y), Y = x +jy+Qn(x, y), where Pn and n are homogeneous polynomials of degree n. For this class of diòerential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.

Original language	English
Pages (from-to)	818-823
Journal	Canadian Mathematical Bulletin
Volume	58
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2015-062-1
Publication status	Published - 1 Dec 2015

Keywords

Diòerential equations on the cylinder
Limit cycles
Polynomial diòerential system

Access to Document

https://doi.org/10.4153/CMB-2015-062-1

https://ddd.uab.cat/record/145301

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abstract = "{\textcopyright} Canadian Mathematical Society 2015. We consider the class of polynomial di{\`o}erential systems of the form x = λx-y+Pn(x, y), Y = x +jy+Qn(x, y), where Pn and n are homogeneous polynomials of degree n. For this class of di{\`o}erential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.",

keywords = "Di{\`o}erential equations on the cylinder, Limit cycles, Polynomial di{\`o}erential system",

author = "Jaume Llibre and Xiang Zhang",

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AU - Zhang, Xiang

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AB - © Canadian Mathematical Society 2015. We consider the class of polynomial diòerential systems of the form x = λx-y+Pn(x, y), Y = x +jy+Qn(x, y), where Pn and n are homogeneous polynomials of degree n. For this class of diòerential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence.

KW - Diòerential equations on the cylinder

KW - Limit cycles

KW - Polynomial diòerential system

U2 - https://doi.org/10.4153/CMB-2015-062-1

DO - https://doi.org/10.4153/CMB-2015-062-1

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JO - Canadian Mathematical Bulletin

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