Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems

We perturb the differential system x˙1=-x2(1+x1), x˙2=x1(1+x1), and x˙k=0 for k=3,…,d inside the class of all polynomial differential systems of degree n in Rd, and we prove that at most nd-1 limit cycles can be obtained for the perturbed system using the first-order averaging theory