Limit cycles bifurcated from a center in a three dimensional system

Abstract

Based on the pseudo-division algorithm, we introduce a method for computing focal values of a class of 3-dimensional autonomous systems. Using the $\epsilon^1$-order focal values computation, we determine the number of limit cycles bifurcating from each component of the center variety (obtained by Mahdi et al). It is shown that at most four limit cycles can be bifurcated from the center with identical quadratic perturbations and that the bound is sharp.

Keywords

• Focal value
• limit cycle
• Hopf bifurcation
• center