# Science:Math Exam Resources/Courses/MATH102/December 2019/Question 08(b)

MATH102 December 2019

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### Question 08(b)

The Allee effect is a phenomenon in ecology by which the per capita reproduction rate of the population increases with increasing population density. In Canada the Allee effect can be observed in the Atlantic cod population in the Gulf of St.Lawrence, where cod is the preferred prey of grey seals. A simple model of the Atlantic cod population growth rate is a modified logistic equation:

$\displaystyle f(N)=N({\frac {N}{2}}-1)(1-N)$ where N is measured in millions of kg of fish. We can assume $N\geq 0.$ The growth rate of the population is given by the differential equation ${\frac {dN}{dt}}=N({\frac {N}{2}}-1)(1-N)$ Use the sketch from part (a) to draw the phase-line diagram(also called state-space) and classify them as stable or unstable. For this part, you can consider negative values of N in addition to the model domain.

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