Week 10 - Nov 12th and 14th
Topics Covered (Lynch, Chapter 5)
11th
Tutorial Quiz Download Tutorial Quiz
12th and 14th
- Limit Sets, Attractors and Separatrix Cycles Download Limit Sets, Attractors and Separatrix Cycles
- Limit Cycles and Poincaré-Bendixon Theory Download Limit Cycles and Poincaré-Bendixon Theory
Recommended Exercises
1. Read Lynch, Chapter 5, and do problems: Section 5.6 -- 1, 2, 3, 4, 6, 7 (g), 8 (a) and 10.
2. Consider the following modification of the predator–prey equations called the Holling-Tanner model (See Example 3 in Section 4.2 of Lynch)
where and are positive constants.
(a) Determine the region in the parameter space of for which this system has a stable equilibrium with both and non-zero.
(b) Using ideas we discussed in the lecture about limit cycles, show that, if the equilibrium point is unstable, this system has a stable limit cycle.
(c) Intepret each of the two cases above in terms of the predator-prey interactions and population dynamics point of view. Explain why this system is a more realistic model of the predator-prey behaviour.