Limit Cycles and Geometric Solutions of a Class of Kukles Differential Systems

In this paper, we provide a complete classification of the global phase portraits for the generalized Kukles differential system [Formula: see text] which is reversible with respect to the [Formula: see text]-axis, with [Formula: see text]. By applying the averaging theory up to the seventh order, we establish the lower bounds on the number of limit cycles that can bifurcate from the center under polynomial perturbations of degree eight.