hw4 - following two ways(i Calculate the eigenvalues of the...

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Applied Dynamical Systems - ME215A Fall 2010 Homework #4 - Due Wednesday October 27, in class 1. (20 pts total) Consider the vector field ˙ x = x - x 2 , (1) ˙ y = - y. (2) (a) (3 pts) What is the ω -limit set and α -limit set for this flow? (b) (3 pts) What is the nonwandering set for this flow? (c) (3 pts) What is the attracting set for this flow? (d) (3 pts) What is the attractor for this flow? Describe the basin of attraction. (e) (8 pts) Show that the attractor for this vector field is asymptotically stable in the
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Unformatted text preview: following two ways. (i) Calculate the eigenvalues of the linearization evaluated at the attractor. (ii) Sketch a trapping region which contains the attractor. Use the functions V 1 ( x, y ) =-1 2 x 2 + 1 3 x 3 (3) and V 2 ( x, y ) = 1 2 y 2 (4) to deduce that this attractor is asymptotically stable. Hint: use the LaSalle Invariance Principle. 1...
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