MATH0030
Answer all questions.
1. Two interacting species with densities X,Y are modelled by the equations
dX
dt = X(a bX cY )(1)
dY
dt = Y ( d + eX), (2)
where a, b, c, d, and e are positive real constants.
(a) Briefly discuss the model, identifying carefully the types of species-species
interactions involved. What is the carrying capacity of the species with den_x005f sity X [Hint: For the carrying capacity, consider the differential equation
for X when Y = 0.]
(b) Re-scale the equations, using the new variables and parameters:
