Linear Phase Portraits: Matrix Entry

The type of phase portrait of a homogeneous linear autonomous system -- a companion system for example -- depends on the matrix coefficients via the eigenvalues or equivalently via the trace and determinant.

9 Responses to “Linear Phase Portraits: Matrix Entry”

  1. kanok on August 27th, 2012 @ 2:30 am

    the demo of phase plane and phase trajetories are very interesting and easy to understand for the system of differential equation. Thank for your demo program.

  2. Annoyed on December 19th, 2014 @ 3:26 am

    Why can't the top rows in the companion matrix be altered? Totally worthless.

  3. hrm on February 5th, 2017 @ 3:12 pm

    The Companion matrix is defined to have top row [0 1].

  4. Ricardo Misturini on May 19th, 2017 @ 11:59 am

    Thank you very much for sharing this app. It helps a lot in the qualitative understanding of the solutions.

  5. Agustin Bejanuel on October 2nd, 2017 @ 9:32 am

    Thank you for this app. It was very useful to see the behavior of a system from a change in its matrix. If you creates an app to plot nonlinear systems, please tell me.

  6. OPL on October 8th, 2017 @ 1:42 pm

    Great App!

  7. hrm on October 13th, 2017 @ 9:21 pm

    Have you looked at Vector Fields?

  8. Hanson Char on November 8th, 2017 @ 3:00 am

    For the companion matrix:

    0 1
    -2 2.5

    The Mathlet arrives at the two real eigenvalues:

    λ1=1.25
    λ2=1.25

    But the eigenvalues should be complex, not real:

    λ1≈1.25+0.66i
    λ2≈1.25−0.66i

    Seems like a bug.

  9. hrm on November 24th, 2017 @ 10:59 am

    Thank you Hanson for pointing this out. I think it has been fixed.

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