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Syllabus
Homework assignments:
HW assignments (collected):
HW 1: Do all problems in the notes (due date Mon 10/19)
HW II: Do the problem on p16 in the notes, Do exercises 2.4.13, 2.4.14, 2.4.16 (read p42-44 first), and 2.4.19 a and b, 3.9.3, and 3.9.16. (due date Mon Nov 16)
HW III: Do problems 4.5.3, 4.5.4 and 4.5.5, and the problems in this file. Due date: Friday Dec 4.
Suggested papers for research projects (grad students only):
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Periodically forced Beverton-Holt model (More background is the following
short paper that generalizes the question to periodic forcing of arbitrary period n. This is known as the Cushing-Henson conjecture, which has been shown to hold in later work.)
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Present Theorems 5.1 and 6.1 from this paper. These results concern the global behavior of
the solutions of the Rosenzweig-Macarthur predator-prey model, which we studied in class. They require the use of a few of other
basic but nontrivial results from the theory of planar dynamical systems (Poincare-Bendixson Theorem, Dulac Theorem, and the unstable manifold Theorem). Please check with me for references on these topics as you will need to at least understand these, and be able to communicate their content during your presentation of the above proofs.
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Present the results from Chapter 19 or from Chapter 20 from these copies
(from the book Mathematics in Population Biology by Horst Thieme, Princeton University Press 2003).
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