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

Question	Answer
r1 < 0 < r2 (real and distinct eigenvalues r1, r2)	Image: One+Negative+One+Positive+Real+Root (binary/octet-stream)
0 < r1 < r2 (real and distinct eigenvalues r1, r2)	nodal source Image: Positive+Distinct+Real+Roots (binary/octet-stream)
r1 < r2 < 0 (real and distinct eigenvalues r1, r2)	nodal sink Image: Negative+Distinct+Real+Roots (binary/octet-stream)
λ = 0 (r1,r2 are complex conjugates r1 = λ + iμ)	Image: Only+Complex+Component+Of+Root (binary/octet-stream)
λ > 0 (r1,r2 are complex conjugates r1 = λ + iμ)	spiral source Image: Positive+Real+Component+Of+Complex+Root (binary/octet-stream)
λ < 0 (r1,r2 are complex conjugates r1 = λ + iμ)	spiral sink Image: Negative+Real+Component+Of+Complex+Root (binary/octet-stream)
r > 0 (r1 = r2, 1 linearly independent eigenvector)	(source) Image: Repeated+Positive+Real+Root+1 Li (binary/octet-stream)
r < 0 (r1 = r2, 1 linearly independent eigenvector)	(sink) Image: Repeated+Negative+Real+Root+1 Li (binary/octet-stream)
r > 0 (r1 = r2, 2 linearly independent eigenvectors)	star node (source) unstable Image: Star+Node+For+Positive (binary/octet-stream)
r < 0 (r1 = r2, 2 linearly independent eigenvectors)	star node (sink) asymptotically stable Image: Star+Node+For+Negative (binary/octet-stream)

Resource summary

	Created by Georgie D'Sanson about 5 years ago