examI_s97

examI_s97 - EE 429 EXAM I 26 February 1997 Name ID DO NOT...

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EE 429 EXAM I 26 February 1997 Name: ID#: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total 100 This test consists of four problems. Answer each problem on the exam itself; if you use additional paper, repeat the identifying information above, and staple it to the rest of your exam when you hand it in. The quality of your analysis and evaluation is as important as your answers. Your reasoning must be precise and clear; your complete English sentences should convey what you are doing. 1

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Problem 1: (25 points) While the behavior of vampires has been studied and documented over long periods of time, the dynamic modeling of vampirism has only been recently addressed. Consider the Lotka-Volterra nonlinear system ˙ v = - av ( t )+ dv ( t ) h ( t ) (1) ˙ h = nh ( t ) - dv ( t ) h ( t ) (2) where h is the stock of humans in an isolated Transylvanian community; v is the number of vampires, a is the death rate of vampires due to contact with sunlight, cruciFxes, garlic, and vampire hunters, n is the growth rate of the human population and d is the contact coeﬃcient. While h and v are functions of time, a , n , and d are constant positive parameters. The term dv ( t ) h ( t ) appearing in equations (1) and (2) means
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examI_s97 - EE 429 EXAM I 26 February 1997 Name ID DO NOT...

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