# 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.