I have a question about the eigenvalues of the prey-predator model called Lotka-Volterra. The model itself consists of 2 nonlinear differential equations of first order:

$$\begin{eqnarray}
 \frac{dx}{dt}&=&ax-bxy \\
 \frac{dy}{dt}&=&cry-dy
\end{eqnarray}$$

I found the stationary points to be both $(0,0)$ and $(d/c, a/b).$ Then I found the eigenvalues (e) to be:

\begin{eqnarray}
e\_1&=&a,\\
e\_2&=&-d,\\
e\_3&=&\pm i\*\sqrt{ad}.
\end{eqnarray}

I know the eigenvalues tells how the system behaves around the stationary points but my question is why are these eigenvalues important for the model? Can they tell something specific about the interaction between the species x and y in the model? I found the eigenvalues but I don't really know to do with them. 

Regards Rasmus O.J
(English is not my native language, so I hope its understandable)