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.
|Journal||Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis|
|Publication status||Published - 8 Feb 2011|
- Averaging method
- Limit cycle
- Periodic orbit
- Reversible center