ws16 - Math 464 Worksheet 16 Consider two populations of...

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Math 464, Worksheet 16 Consider two populations of animals that compete for space and/or other resources. Either population alone would expand to the limits of its environment, but together each population exerts a negative influence on the other. This is represented by b x b y d x d y (-) (-) y x For this exercise we will assume: Birth rate of species x is b x = 0 . 02 animals per week. Birth rate of species y is b y = 0 . 03 animals per week. Death rate of species x is d x = 0 . 01 x animals per week. Death rate of species y is d y = 0 . 01 y animals per week. The effect of y on x is that each week 0 . 01 xy of species x die off. The effect of x on y is that each week 0 . 02 xy of species y die off. 1. Write difference equations for the populations x and y . 2. Assume that x (0) = 0. Use qualitative analysis to graph the population y ( t ) on t - y axes for each of: (a) y (0) = 1 (b) y (0) = 3 (c) y (0) = 5 3. For each initial population in Problem 2, graph ( x ( t ) ,y ( t )) as a parametric function on x - y axes. 4. Assume that y (0) = 0. Use qualitative analysis to graph the population x ( t ) on t - x axes for each of: (a) x (0) = 0 1
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(b) x (0) = 1 (c) x (0) = 2 (d) x (0) = 3 (e) x (0) = 4 5. For each initial population in Problem 4, graph (
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