Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3
Lopes, Bruno D.
de Moraes, Jaime R.
Texas State University, Department of Mathematics
In this article we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. Then the maximum number of limit cycles that bifurcate from these periodic orbits is 6 and it is reached. This family of of centers completes the study of the limit cycles which can bifurcate from periodic orbits of all centers of the weight-homogeneous polynomial differential systems of weight-degree 3 when perturbed in the class of all polynomial differential systems having the same degree and whose average function of first order is not zero.
Polynomial vector field, Limit cycles, Averaging method, Weight-homogeneous differential system
LLibre, J., Lopes, B. D., & de Moraes, J. R. (2018). Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3. <i>Electronic Journal of Differential Equations, 2018</i>(118), pp. 1-14.
Attribution 4.0 International