Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems

摘要

Perturbing the system $dot{x} = - y{left( {1 + x} right)},,dot{y} = x{left( {1 + x} right)},,dot{z} = 0$ inside the family of polynomial differential systems of degree n in $mathbb{R}^{3}$ , we obtain at most n 2 limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n 2 limit cycles.