Abstract and Applied Analysis

Poincaré Bifurcations of Two Classes of Polynomial Systems

Abstract

Using bifurcation methods and the Abelian integral, we investigate the number of the limit cycles that bifurcate from the period annulus of the singular point when we perturb the planar ordinary differential equations of the form $\dot{x}=-yC(x,y)$, $\dot{y}=xC(x,y)$ with an arbitrary polynomial vector field, where $C(x,y)=1-{x}^{3}$ or $C(x,y)=1-{x}^{4}$.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 861329, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449391

Digital Object Identifier
doi:10.1155/2013/861329

Mathematical Reviews number (MathSciNet)
MR3090275

Zentralblatt MATH identifier
07095443

Citation

Wang, Jing; Shui, Shuliang. Poincaré Bifurcations of Two Classes of Polynomial Systems. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 861329, 12 pages. doi:10.1155/2013/861329. https://projecteuclid.org/euclid.aaa/1393449391

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