Is there a non constant entire function $\gamma(t)=(x(t),y(t)): \mathbb{C} \to \mathbb{C}^{2}$ which satisfy the following Vander pol dififferential equation?

$$\begin{cases}\dot{x}=y-x^{3}\\\dot y=-x\end{cases}$$

For a related question see the last part of the following post:

The error in Petrovski and Landis' proof of the 16th Hilbert problem