Unformatted text preview: Homework assignment 2 * February 3, 2006 1. Explain the occurence of an inflection point in the solutions of the Verhulst equation that have initial conditions in the interval (0 , K/ 2), where K is the carrying capacity. Do this without using the explicit expression for the solution we derived in class. 2. The Allee effect says that for very small population numbers, the population will not be viable and go extinct. That is, there is some small ǫ > 0 such that if N (0) ∈ (0 , ǫ ), then N ( t ) → 0 as t → ∞ . Write down the simplest possible continuous-time population model dN/dt = NF ( N ) you can think of that exhibits the Allee effect, but behaves like the Verhulst equation otherwise (that is, there is some carrying capacity K to which all solutions -except for those in [0 , ǫ ]- converge as t → ∞ ). 3. Verify all the calculations we skipped in class regarding the interpretation of the inverse of the dilution rate in the chemostat model....
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
- Summer '06