It was proven that if the quadratic system inside the polynomial systems of degree n is perturbed, a first order in ε at most n limit cycles can be obtained. There are essentially three methods for studying the bifurcated limit cycles from a center. They are based on the Poincare return map, on the Poincare-Pontrjagin-Melkinov integrals or abelian integrals that are equivalent in the plane and on the inverse integrating factor. The averaging theory is used to study the bifurcated limit cycles.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Oct 2001|
- Bifurcation from a center
- Limit cycles