527ass7 - 642:527 ASSIGNMENT 7 FALL 2009 Turn in starred...

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Unformatted text preview: 642:527 ASSIGNMENT 7 FALL 2009 Turn in starred problems Tuesday 10/27/2009. Section 7.4: 2 (a), (b)*, (f)* See instructions below. Section 7.4: 7 Section 7.5: 4* Problem 7.A* Two interacting populations x ( t ) , y ( t ) are described by the equations x = (1- x ) x , y = (3- y- x ) y . (a) Find all the critical points of this system. You do not need to classify these. (b) Sketch the first quadrant x 0, y 0 of the phase plane, indicating, by arrows or other- wise, regions where x and y are increasing, x is increasing and y decreasing, etc., and where the trajectories are horizontal and vertical. (c) For each initial condition below, find (from your sketch or otherwise) lim t bracketleftbigg x ( t ) y ( t ) bracketrightbigg : (i) x (0) = 0 , y (0) = 1; (ii) x (0) = 3 , y (0) = 3; (iii) x (0) = 0 , y (0) = 0. In 7.4 (b), (f), please do the following: Find all singular points; Obtain the linearized system near each singular point and classify the origin of that system (as...
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