Fixed Point of a 2x2 Linear System of ODEs
Fixed Point of a 2x2 Linear System of ODEs
This Demonstration shows trajectories in the linear autonomous system
=
x |
y |
4 | k |
-1 | 2 |
x |
y |
for various values of the parameter . Different values of are associated with the different types possible for the fixed point at the origin. For , the fixed point is an unstable spiral; for , it is an unstable improper node; for , it is an unstable node; for , it is a saddle.
k
k
k>1
k=1
-8<k<1
k<-8
When the eigenvalues of the matrix are real, orange lines are shown that are parallel to the eigenvectors.