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Phase Portrait Question

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

    dx/dt=y-x

    dy/dt=x-y

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

    f(x,y)=x+y

    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

    arildno

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    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.
     
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