Eigenvalues and Linear Phase Portraits

′



x

y







-1	1
0.5	-1





x

y



a

11

-1

a

12

1

a

21

0.5

a

22

-1

This shows the phase portrait of a

2×2

linear differential system along with a plot of the eigenvalues of the system matrix in the complex plane.

Details

Sliders allow manipulation of the matrix entries over

[-2,2]

. By viewing simultaneously the phase portrait and the eigenvalue plot, one can easily and directly associate phase portrait bifurcations with changes in the character of the eigenvalues.

External Links

Eigenvalue (Wolfram MathWorld)

Phase Portrait (Wolfram MathWorld)

Permanent Citation

Selwyn Hollis

"Eigenvalues and Linear Phase Portraits"
http://demonstrations.wolfram.com/EigenvaluesAndLinearPhasePortraits/
Wolfram Demonstrations Project
Published: March 22, 2010