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Calculus 1 - Assignment 2

# Calculus 1 - Assignment 2 - Pawel Lorek University of...

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Pawesuppressl Lorek, University of Ottawa, MAT 1330D, Winter 2009 Assignment 2, due March 4, 17:30 in class Student Name Student Number Problem 1: [4 points] Consider the following DTDS: M t +1 = 8 M 2 t 15 + M 2 t Analyze this DTDS, i.e., determine the biologically relevant fixed points (i.e. equilibria) and their stability. Draw the updating function and use cobwebbing to illustrate and confirm your analytical results. Problem 2: [8 points] Consider the following nonlinear DTDS for growing population with harvesting: x t +1 = f ( x t ) = 4 x t (3 - x t ) - hx t , where h 0 denotes the intensity of harvesting. (a) [4p] Analyze this DTDS, i.e., determine the biologically relevant fixed points and their stability. Summarize your results in the form of a little table: range of h fixed point(s) stability (b) [2p] Draw the updating function and use cobwebbing for h = 10
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