Consider an ecosystem composed of mice, owls, and foxes. The mice have an ample
ID: 2847378 • Letter: C
Question
Consider an ecosystem composed of mice, owls, and foxes. The mice have an ample food supply but are preyed upon by both the owls and foxes. Let x(t), Y(t), and z(t) denote respectively the mouse, owl, and fox populations at time t. Obtain the system of differential equations that governs the population dynamics of each species if the mice compete among themselves for food, the owls compete among themselves and with the foxes for mice, and the foxes compete among themselves and with the owls for mice.
Please show steps and explain how you got there so I can understand the logic.
Explanation / Answer
x(t)= x0-ky(t)-lz(t)-mx(t-1)
y(t)=y0-ny(t-1)-oz(t-1)
z(t)=z0-oy(t-1)-pz(t-1)