Hyperbolicity and Averaging for the Srzednicki-W\'ojcik equation

For the Srzednicki-W\'ojcik equation, the planar nonautonomous ODE parameterized by $\kappa \in \mathbb{R}$, $$ z'=\overline{z}(1+ |z|^2 \exp(i \kappa t)), \qquad z(t) \in \mathbb{C} $$ using averaging we show how the region of hyperbolicty grows with $|\kappa|$. Based on this we give bounds on the sizes of bounded orbits.