Consider two species whose survival depends on their mutual cooperation. Let's take as an example a species of bee that feeds primarily on the nectar of one plant species and simultaneously pollinates that plant. One simple model of this mutualism is given by the autonomous system:

a. What assumptions are implicitly being made about the growth of each species in the absence of cooperation?

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

c. What are the equilibrium levels?

d. Perform a graphical analysis and indicate the trajectory directions in the phase plane.

e. Find an analytic solution and sketch typical trajectories in the phase plane.

f. Interpret the outcomes predicted by your graphical analysis. Do you believe the model is realistic? Why?

Transcribed Image Text:

-my +nxy dt dy IP Axq + xp-= xp