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 $\displaystyle \frac{dC}{dt}=aC-bCW, \qquad \frac{dW}{dt}=-cW+dCW$.

(a) What values of $dC/dt$ and $dW/dt$ correspond to stable populations?
(b) Suppose $a=.05, b=.01, c=.05, d=.0001$. After finding population pairs $(P,C)$ that lead to stable populations, is it possible for the species to live in balance or both species become extinct? Answer "b" for balance and "e" for extinction.

(a)
(b)