The authors apply the “gluing” method to construct planar polynomial systems of the form
with “large” numbers of limit cycles or singular points. For example, they show that there exists an absolute constant with the following property: it is possible to construct a system with having at least
limit cycles. They also show that, for any nonnegative integer numbers and satisfying the conditions
it is possible to construct a system with having imaginary singular points, attractors, repellers, and saddles.