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

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