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Unformatted text preview: Homework 8, Solutions page 285, problem 8.1.10: a) The average size S of the trees grows logistically, but with a carrying capacity that depends on the health of the forest: The carrying capacity is E K E K S , where K S denotes the equilibrium value of S when E is at its “carrying capacity” K E . Typ- ically, E will be less than K E , and as a result the carrying capacity of S will be less than K S . At the same time, E also follows a logistic law, with “carrying capacity” K E , but in addition it is driven down by the term- P B S . Note that the ratio B / S is proportional to the density with which budworms populate trees. b) “Non-dimensionalize” is a slightly problematic word here. Which units should be assign to E , for instance? But non-dimensionalization really means writing the equation in such a way that the number of parameters that appear is as small as possible. This we can do. We simply write: t = t ˜ t , S = S ˜ S , E = E ˜ E , where t , S , and E should be thought of as the units in which we will measure...
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- Spring '09
- KE, Ks, Bifurcation theory, KE KE S0