Consider the competitive hunter model defined by: a.What assumptions are implicitly being made about the growth of

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Consider the competitive hunter model defined by:

dx dt dy dt = a(1-x/k)x-bxy m(1-y/k)y-nxy where x represents the trout population and y the bass population.

a. What assumptions are implicitly being made about the growth of trout and bass in the absence of competition?

b. Interpret the constants a, b, m, n, k1, and k2 in terms of the physical problem.

c. Perform a graphical analysis and answer the following questions:

i. What are the possible equilibrium levels?
ii. Is coexistence possible?
iii. Pick several typical starting points and sketch typical trajectories in the phase plane.
iv. Interpret the outcomes predicted by your graphical analysis in terms of the constants a, b, m, n, k1, and k2.

When you get to step (i), you should realize that at least five cases exist. You will need to analyze all five cases. One case is when the lines are coincident.

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Related Book For  book-img-for-question

A First Course In Mathematical Modeling

ISBN: 9781285050904

5th Edition

Authors: Frank R. Giordano, William P. Fox, Steven B. Horton

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