7. Suppose you are studying a system of differential equations, and you find an unstable spiral...
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7. Suppose you are studying a system of differential equations, and you find an unstable spiral equilibrium point. You also find a trajectory that makes a complete loop around that equilibrium point. In a 2D state space, these conditions usually cause that "loop trajectory" to be a limit cycle attractor. a) If the state space is three-dimensional, does the loop have to be a limit cycle attractor? Explain. b) Can you think of a way that these conditions could occur in a 2D state space so that the loop is not a limit cycle attractor? Explain. A picture is a good idea. (Hint: It can happen, but it's extremely unlikely.) 7. Suppose you are studying a system of differential equations, and you find an unstable spiral equilibrium point. You also find a trajectory that makes a complete loop around that equilibrium point. In a 2D state space, these conditions usually cause that "loop trajectory" to be a limit cycle attractor. a) If the state space is three-dimensional, does the loop have to be a limit cycle attractor? Explain. b) Can you think of a way that these conditions could occur in a 2D state space so that the loop is not a limit cycle attractor? Explain. A picture is a good idea. (Hint: It can happen, but it's extremely unlikely.)
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a If the state space is threedimensional the loop does not have to be a limit cycle attractor In thr... View the full answer
Related Book For
Systems Analysis and Design
ISBN: 978-1133274636
9th Edition
Authors: Shelly Cashman, Gary B. Shelly and Harry J. Rosenblatt
Posted Date:
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