Fixed Point of a 2x2 Linear System of ODEs

k

This Demonstration shows trajectories in the linear autonomous system





x



y

=

4	k
-1	2



x

y



for various values of the parameter

k

. Different values of

k

are associated with the different types possible for the fixed point at the origin. For

k>1

, the fixed point is an unstable spiral; for

k=1

, it is an unstable improper node; for

-8<k<1

, it is an unstable node; for

k<-8

, it is a saddle.

When the eigenvalues of the matrix are real, orange lines are shown that are parallel to the eigenvectors.