Populations of aphids and ladybugs are modeled by the equations LA 400- -0.5L + 0.0001AL (a) Find the equilibrium solutions and explain their significance. (b) Find an expression for dL/dA. (c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common? 300+ 200 100- dA dt … -- 24 -0.01AL dL dt 5000 TELEZ-NIAL 10000 15000 A (d) Suppose that at time=0 there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change. (e) Use part (d) to make rough sketches of the aphid and ladybug populations as functions of t. How are the graphs related to each other?

Populations of aphids and ladybugs are modeled by the equations LA 400- -0.5L + 0.0001AL (a) Find the equilibrium solutions and explain their significance. (b) Find an expression for dL/dA. (c) The direction field for the differential equation in part (b) is shown. Use it to sketch a phase portrait. What do the phase trajectories have in common? 300+ 200 100- dA dt … -- 24 -0.01AL dL dt 5000 TELEZ-NIAL 10000 15000 A (d) Suppose that at time=0 there are 1000 aphids and 200 ladybugs. Draw the corresponding phase trajectory and use it to describe how both populations change. (e) Use part (d) to make rough sketches of the aphid and ladybug populations as functions of t. How are the graphs related to each other?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.EA: Extended Application Managing Renewable Resources

Problem 1EA: Suppose that a particular plot of land can sustain 500 deer and that the population of this...

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