Homework 6

Homework 6 - Homework 6 Due October 28th, 2008. Problem 1...

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Unformatted text preview: Homework 6 Due October 28th, 2008. Problem 1 Problem 2 Challenge “Goal‐seeking Behavior” on page 281 of the textbook. Consider the following stock and flow diagram: Fish Regenerate Caught g Carrying Capacity This model captures the dynamics of fish regeneration using a very simple assumption: fish regeneration goes down linearly as the fish reaches the system’s carrying capacity. The equation used in the model are: Regenerate(t) = g*Fish(t)*(1‐Fish(t)/CarryingCapacity) with Carrying Capacity, g, and Caught being constants. a) If Caught has been fixed, what are the two equilibrium states for this system? Answer this question for all possible values of g, Caught, and Carrying Capacity, i.e., find a general formula for the two equilibrium states. b) Use iThink, to 1) verify that the states are indeed equilibria. To do this set the initial value of the Fish stock to your answer to part a). Suggested values for the constants are Carrying Capacity=2000, g=2, and Caught=500. c) Use iThink to find which of these two equilibrium states is stable, and which one is unstable. To do this change the initial value of the Fish stock up or down a little (e.g., .01), and observe the resulting system behavior. Does the Fish stock return to the equilibrium point (stable), or does it diverge (unstable)? d) Given values of g and Carrying Capacity, what is the maximum sustainable value for Caught? Find a general algebraic expression for this (use calculus). For this value of Caught, what is the only equilibrium state? Is it stable or not? e) Verify part d) using iThink. Turn in your solutions written by hand, and a printout of your verifications (parts b), c), and e)). ...
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This note was uploaded on 01/02/2010 for the course EMSE 235 taught by Professor Enriquescamposnanez during the Fall '08 term at GWU.

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