Suppose we have three species interacting with each other: x is a predator and y

Question

Suppose we have three species interacting with each other: x is a predator and y and z are both its prey. Assume the following: x dies out in absence of its prey (at rate a=7/8), y grows exponentially at rate b=1/4 in absence of predator, z grows logistically in absence of predator (at growth rate c=1/3 and carrying capacity K=2), and changes in population due to interactions are proportional to the number of possible interactions between the species (Rates=1). Build the model and find equilibrium points.

Explanation / Answer

x= -7t/8

y =e^(7t/8)

Z =2ln(t)/3

population(t) = -7t/8 +e^(7t/8) + 2ln(t)/3

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