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Unformatted text preview: Practice Exam 2: MAP 4305 1. Determine stability of the equilibrium at (0, 0) of x = y 3 - 2x3 y 2. Let A= = -3x - y 3 1 , x0 = t 0 . 1 1 2 2 ,b = 1 First find etA . Next, using the variation of constants formula, solve x = Ax + b, x(0) = x0 3. Let V : R2 R be a twice continuously differentiable function. Consider the system x = Vx (x, y) y = Vy (x, y) Let (x , y ) be a critical point of V (ie Vx (x , y ) = Vy (x , y ) = 0). Then (x , y ) is clearly an equilibrium point of the system. Can it be a spiral (stable or unstable) or a center? 4. Find the nullclines and equilibria of x = x(1 - x - 0.5y) y = y(1 - 0.5x - y) Linearize at each equilibrium to determine its nature, and perform phase plane analysis. Instructor: Patrick De Leenheer. 1 ...
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This note was uploaded on 04/07/2008 for the course MAP 4305 taught by Professor Deleenheer during the Spring '06 term at University of Florida.
- Spring '06