Limit Cycles for a Perturbation of a Quadratic Center with Symmetry

作者：Cherkas L A^*

来源：Differential Equations, 2011, 47(8): 1077-1087.

DOI：10.1134/S0012266111080015

To estimate the number of limit cycles appearing under a perturbation of a quadratic system that has a center with symmetry, we use the method of generalized Dulac functions. To this end, we reduce the perturbed system to a Lienard system with a small parameter, for which we construct a Dulac function depending on the parameter. This permits one to estimate the number of limit cycles in the perturbed system for all sufficiently small parameter values. We find the Dulac function by solving a linear programming problem. The suggested method is used to analyze four specific perturbed systems that globally have exactly three limit cycles [i.e., the limit cycle distribution 3 or (3, 0)] and two systems that have the limit cycle distribution (3, 1) (i.e., one nest around each of the two foci).

• 出版日期2011-8