lab_11_expectations - 5. Use your previous answer to prove...

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Lab 11 – Linear Systems Expectations 1. Find the equilibrium points for (*). 2. Show that the eigenvalues are as shown in the lab. Using fplot, plot y=x²/4 for |x|<4 and |y|<4. Label the T and D axes. a) Indicate on the plot the points for which the eigenvalues are not real (NR). b) Fill in the other regions as prescribed. 3. Pick a point (T,D) in the PP region and enter the system (***) into pplane. Plot several orbits and describe their behavior, specifically questions a and b. 4. Find the general solution to (***) with the same (T,D) values from 3.
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Unformatted text preview: 5. Use your previous answer to prove that your answer from 3a would be valid for any solution where (T,D) is in the PP region. 6. Choose a point (T,D) in the region NN and repeat parts 3 and 4. 7. Choose a point (T,D) in the region NP and repeat parts 3 and 4. 8. Find examples of points (T,D) in NR that satisfy: a) a spiral sink b) a spiral source c) a center at the origin Plots: 2, 3, 6, 7, 8 (3 points on 1 plot is fine)...
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This note was uploaded on 06/20/2011 for the course MA 366 taught by Professor Arielbarton during the Spring '11 term at Purdue University Calumet.

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