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# ws18 - 1(l(4 1(m(5 1 4 Adjust the model so that...

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Math 464, Worksheet 18 Alter the population model from Worksheet 17 so that the two species cooperate: Δ x = 0 . 02 x - 0 . 01 x 2 + 0 . 01 xy Δ y = 0 . 03 y - 0 . 01 y 2 + 0 . 02 xy 1. Locate all equilibria. 2. For each equilibrium point: (a) linearize (b) find eigenvectors (c) sketch them on one sheet of graph paper. 3. For each initial population shown below, sketch the graph of ( x ( t ) ,y ( t )) as a parametric function. Use your eigenvectors and equilibria as a guide. Check yourself using Excel. You can crib my Worksheet 16 solution as a starting point . (a) (0 . 1 , 0 . 1) (b) (0 . 1 , 1) (c) (0 . 1 , 3) (d) (0 . 1 , 5) (f) (1 , 5) (g) (2 , 5) (h) (3 , 5) (i) (4 , 5) (j) (5 , 5) (j) (2
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Unformatted text preview: , 1) (l) (4 , 1) (m) (5 , 1) 4. Adjust the model so that interactions are good for species x but bad for species y . (Perhaps species x is foxes and species y is rabbits. Interaction is good for foxes — dinner — and corresponding bad for rabbits.) Δ x = 0 . 02 x-. 01 x 2 + 0 . 01 xy Δ y = 0 . 03 y-. 01 y 2-. 02 xy Repeat Problems 1-3 for this model. 5. Switch the good/bad interactions: Δ x = 0 . 02 x-. 01 x 2-. 01 xy Δ y = 0 . 03 y-. 01 y 2 + 0 . 02 xy Repeat Problems 1-3 for this model. 1...
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