A Predator-Prey System Is Modeled by the System of Differential $\frac { d x } { d t } = a x - b x y$

question 13

Essay

A predator-prey system is modeled by the system of differential equations $\frac { d x } { d t } = a x - b x y$ , $\frac { d y } { d t } = - c y + d x y$ , where a, b, c, and d are positive constants.(a) Which variable, x or y, represents the predator? Defend your choice.(b) Show that the given system of differential equations has the two equilibrium solutions $\{ x + 0 , y = 0 \}$ and $\left\{ x = \frac { c } { d } , y = \frac { a } { b } \right\}$ .(c) Explain the significance of each of the equilibrium solutions.

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