# Chapter 11, Application 47

Now do another investigation of the Predator-Prey equations but this time with $$\beta = \frac{1}{5}$$.

• Explain why there are still fixed points at (0,0) and ($$\frac{1}{2}$$,0) and why the dynamics on each axis is identical to the previous model.
• Find the value of the third fixed point. How has reducing the value of $$\beta$$ affected the equilibrium predator and prey populations? Interpret these changes in terms of the model.
• Compute $$DF$$ and evaluate it at this new fixed point. Find the eigenvalues. How has the stability changed if at all?