Math 130 Final Quiz 5
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Math 130 Jekel
Final Quiz 5
March 22, 2023
Question 1 (3 points). Find all equilibria of the system 
Question 2 (3 points). Consider the system 
which has an equilibrium at (0, 0).
(a) Compute the Jacobian at the equilibrium. (b) What type of equilibrium does the linearized system have?
(c) What can you conclude about the equilibrium of the nonlinear system from the linearization?
Question 3 (2 points). (a) classify the equilibria, (b) find a closed orbit, and (c) find a homoclinic orbit. Arrows show the vector field, blue curves show trajectories, red points are equilibria.
Question 4 (2 points).
(a) Consider the vector field (f,g) and the blue curve C in the picture below left. Compute the index of C
visually by tracking the changes in the vector field along C .
(b) Suppose that the system x˙ = f(x,y) and y˙ = f(x,y) has equilibria arranged as in the diagram below
right. Draw a simple closed curve C which will have index 3.
(a)
(b)
2023-03-25