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?