Lotka-Volterra with logistic term

Question

I have the following predator-prey system $$V'=rV(1-V/K)-aVP,$$ $$P'=-sP+abVP.$$ After some manipulations i end up with the adimensional system $$x'=x(1-\gamma x-y),$$ $$y'=y(-\beta+x),$$ where $\beta=s/r$ and $\gamma=r/(abK)$. I want to study the steady points, which are $(0,0), (1/\gamma,0)$ and $(\beta,1-\gamma\beta)$. From the jacobian matrix i can conclude that $(0,0)$ is a saddle point, but the other two points give me some difficult eigenvalues which i'm not able to classify. How can i study these points? Any help will be very appreciated. The jacobian matrix for the critical points are $$J(1/\gamma)=\begin{pmatrix} -1&-1/\gamma\\0&1/\gamma-\beta\end{pmatrix},$$ and $$J(\beta,1-\gamma\beta)=\begin{pmatrix}-\gamma\beta&-\beta\\1-\gamma\beta&0\end{pmatrix}$$