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Unformatted text preview: MS&E 201 Dynamic Systems Final Exam, Page 1 of 8 Spring 04-05 June 8, 2005 Professor Edison Tse MS&E 201 DYNAMIC SYSTEMS FINAL EXAM 2004-2005 THREE HOURS 180 minutes, total 100 points. Open Book. Open Notes. Write your name on this page of the exam. You will be turning in the exam questions with your answers. However, we will not consider anything except what is written in the blue books in grading your exam. Please read and sign the Honor Code on all blue books you use or we will not grade the exam. No programmable calculators or computers are permitted at the examination. Calculations will be kept as simple as possible, and you will receive most of the credit for setting up calculations correctly, even if you do not carry them out. Partial credit will be given whenever possible, provided your solution is neat and clear. Please do not open the examination until everyone is ready and you are asked to begin. At that time please check to see that your exam contains 8 pages with 6 questions. MS&E 201 Dynamic Systems Final Exam, Page 2 of 8 Spring 04-05 June 8, 2005 Professor Edison Tse 1. Basic concepts. (True or False. Explanation is not necessary, total 28 points) (1) In Creating a New Game in Business Competition, the failure of People Express Airline in 1988 was because big airlines such as UA and AA fought back by also providing the same no-frills, low-fare air travel services. (2) In cusp catastrophe dynamic systems, there will always be three equilibrium points, two of which are stable while the middle one is unstable. (3) In the predator-prey model discussed in class, eventually only one species will survive. (4) Suppose you are using the linearization method to determine the stability of an equilibrium point in a continuous time non-linear dynamic system. If all the eigenvalues of the Jacobian matrix evaluated at the equilibrium point are real and the largest eigenvalue is zero, then the equilibrium point is marginally stable. (5) Consider the system b k Ax k x + = + ) ( ) 1 ( . If all the eigenvalues of A are less than 1 in magnitude, then the state vector will eventually be aligned with the vector b. (6) In a non-linear dynamic system, there may be several asymptotically stable equilibrium points. (7) Consider a continuous , time-invariant , dynamic system with no input . Judge the following statements as either true or false. a). Finding the local stability properties of a nonlinear system is equivalent to finding the stability properties of a linearized system at the equilibrium point....
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