Limit cycles for the class of \(D\)-dimensional polynomial differential systems
Summary: We perturb the differential system \(\dot{x}_1=-x_2(1+x_1)\), \(\dot{x}_2=x_1(1+x_1)\), and \(\dot{x}_k=0\) for \(k=3,\dots, d\) inside the class of all polynomial differential systems of degree \(n\) in \(\mathbb R^d\), and we prove that at most \(n^{d-1}\) limit cycles can be obtained for the perturbed system using the first-order averaging theory.
scientific article; zbMATH DE number 7037268