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Unformatted text preview: Applied Dynamical Systems - ME215A Fall 2010 Homework #2- Due Wednesday Oct 13th in class 1. (5 pts total) Suppose M = A B D ! . (1) Verify that the eigenvalues of M are A and D , with associated eigenvectors (1 , 0) T and ( B/ ( D- A ) , 1) T , respectively. 2. (45 pts total) Consider the vector field which models the interaction between a predator population ( p ( t )) and a prey population ( v ( t ), for victim): ˙ v = v ( a- ev- bp ) (2) ˙ p = p (- c + dv ) . (3) The parameters a,b,c,d,e are all positive and real. We assume that ad- ce > 0. Only non- negative values of v and p are biologically relevant, with zero corresponding to extinction of that species. The assumptions in the model are: (i) In the absence of predation, the prey population grows exponentionally when the prey population is small: this is the av term. (ii) In the absence of predation, the prey population saturates through competition for resources: this is the- ev 2 term....
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This note was uploaded on 12/29/2011 for the course ME 215a taught by Professor Moehlis,j during the Fall '08 term at UCSB.
- Fall '08