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ptest4 - ˙ x = y 2-1 ˙ y = x 3-y a 2 ˙ x = xy-2 ˙ y =...

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1 Practice Problems for Test 4 of Math1502KB 1. Find the solution of the following linear system with initial condition (a) ˙ x = 2 x + y , x (0) = 0 ˙ y = x + y , y (0) = 1 (b) ˙ x = 4 x - 3 y , x (0) = 1 ˙ y = 6 x - 7 y , y (0) = 2 (c) ˙ x = x - 2 y , x (0) = 2 ˙ y = x - y , y (0) = 2 2. Identify the equilibrium point (0 , 0) of the following linear systems and study its stability. (a) ( a 1) ˙ x = - 2 x - 2 y ˙ y = x , ( a 2) ˙ x = x + 2 y ˙ y = 2 x + y (b) ( b 1) ˙ x = ε x + ε y ˙ y = - x ε 0 , ( b 2) ˙ x = x - ε y ˙ y = ε x - y ε ± 1 . 3. Find and Identify all the equilibrium point of the following nonlinear systems and study their stability. (a) ( a 1)
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Unformatted text preview: ˙ x = y 2-1 ˙ y = x 3-y , ( a 2) ˙ x = xy-2 ˙ y = x-2 y (b) ( b 1) ˙ x = y ˙ y = sin x-y , ( b 2) ˙ x = x-y ˙ y = x 2-y . 4. Study the following Lotka-Volterra system at ε =-1 , , 1. ˙ x = 2 x-xy + ε x (5-y ) , ˙ y =-5 y + xy , What does your analytical results tell you about this system? 5. 11.3.11-18, 11.4. 3-10, 22-26, 45-48...
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