Hare and Lynx Demonstration

The dynamics of the Hare and Lynx predator/prey system provides a very useful illustration of phase plane analysis for a system of two ordinary differential equations. The textbook includes a discussion of this example in Section 3.7

Under the downloads you will find a link to a compressed folder holding with Matlab and Simulink files for demonstrating the Hare/Lynx dynamics. The files include a Simulink model, and a separate Matlab script with which you can explore this system.

The qualitative concepts you should learn from this example include

• Phase plane modeling in Simulink and Matlab
• Time invariant differential equations as vector fields in phase space.
• Nullclines, Steady States, and Limit Cycles
• Linearization
• Global versus local stability

To test your understanding, consider the following questions:

1. What do the three steady states represent in terms of the Hare/Lynx populations?
2. Repeat the simulations setting the parameter b = 0.26. How do the results change?
3. Repeat again for b = 0.20.  What happened to the third steady state? Interpret this in terms of the Hare/Lynx population dynamics.
4. What is the critical value of b for which a limit cycle first appears?
5. What is the critical value of b for which the linear approximation first exhibits complex eigenvalues? How do you interpret this situation?