evaluating locally linear systems (stability, type, phase portrait)

Flashcards by Georgie D'Sanson, created more than 1 year ago

We want to solve x' = Ax. If detA =/= 0, then the origin is the only critical point. The following are different classifications of the zero vector for type and stability with corresponding phase portraits.

	Created by Georgie D'Sanson over 5 years ago

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r1 < 0 < r2

(real and distinct eigenvalues r1, r2)

0 < r1 < r2

(real and distinct eigenvalues r1, r2)

r1 < r2 < 0

(real and distinct eigenvalues r1, r2)

λ = 0

(r1,r2 are complex conjugates r1 = λ + iμ)

λ > 0

(r1,r2 are complex conjugates r1 = λ + iμ)

λ < 0

(r1,r2 are complex conjugates r1 = λ + iμ)

r > 0

(r1 = r2, 1 linearly independent eigenvector)

r < 0

(r1 = r2, 1 linearly independent eigenvector)

r > 0

(r1 = r2, 2 linearly independent eigenvectors)

r < 0

(r1 = r2, 2 linearly independent eigenvectors)