Consider the competitive hunter model defined by:

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.

Transcribed Image Text:

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.