Problem 35E

35. 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

$$ \frac{d C}{d t}=a C-b C W \quad \frac{d W}{d t}=-c W+d C W $$

(a) What values of $d C / d t$ and $d W / d t$ correspond to stable populations?

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

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