Textbook Problem

In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern Canada. The interaction has been modeled by the equations

$\frac{dC}{dt}=aC-bCW\frac{dW}{dt}=-cW+dCW$

(a) What values of dC/dt and dW/dt correspond to stable populations?

(b) How would the statement “The caribou go extinct” be represented mathematically?

(c) Suppose that a = 0.05, b = 0.001, c = 0.05, and d = 0.0001. Find all population pairs (C, W) that lead to stable populations. According to this model, is it possible for the two species to live in balance or will one or both species become extinct?