The interaction of two populations x(t)and y(t)is modeled by the system $\frac{1}{x} \frac{d x}{d t}=1-x-k y, \frac{1}{y} \frac{d y}{d t}=1-y+k x$ , where k is a positive constant.What type of interaction is modeled here?
A)Symbiosis
B)Predator-Prey with y the predator and x the prey.
C)Predator-Prey with x the predator and y the prey.
D)Competition
E)None of the above

Question

Quizplus · Accepted Answer

The system of equations is a predator-prey model where the growth rate of each population depends on the presence of the other. The term "-ky" in the equation for x indicates that y negatively affects x, suggesting y is the predator. The term "+kx" in the equation for y indicates that x positively affects y, suggesting x is the prey.

The Interaction of Two Populations X(t)and Y(t)is Modeled by the System