Publication

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Paper

# On the limit cycles of polynomial vector field

## Abstract

In this paper we study the limit cycles which can bifurcate from the periodic orbits of the center located at the origin of the quadratic polynomial di®erential system x = -y(1+x), y= x(1+x), and of the cubic polynomial di®erential system x = -y(1-x2-y2), y= x(1-x 2-y2), when we perturb them in the class of all polynomial vector fields with quadratic and cubic homogenous nonlinearities, respectively. For doing this study we use the averaging theory. Copyright © 2011 Watam Press.