Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Phase Portrait Question

  1. Apr 29, 2004 #1
    Hello, I'm considering the system:



    I've found the fixed points and shown that this is a first integral of the system:


    How can I (using this information only) sketch a phase portrait? I know the graph of fixed points looks like the x=y graph, but im not sure how this relates to a phase portrait.

    Any help? Thanks.
  2. jcsd
  3. Apr 29, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    From my slight acquaintance with phase portraits( among lots of other stuff..), I'd say the
    equations f(x,y)=x+y=const. for different constants defines your phase portrait.
    In particular, it would be important to graph whether solutions converge towards some fixed point at x=y (i.e stable fixed points), or if the fixed points are unstable/saddle-like.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook