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Math Help - Saddles and Nodes

  1. #1
    Super Member Deadstar's Avatar
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    Saddles and Nodes

    Hello,

    I have a phase portrait that is supposed to contain a saddle and a node, only problem is i can only see the saddle which is at about 0.25. Could someone point out where the node is? I know the pictures not that great and if you want another view just say.
    Thanks
    Attached Thumbnails Attached Thumbnails Saddles and Nodes-0.5a.jpeg  
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  2. #2
    Super Member Showcase_22's Avatar
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    Can you post the equation that you're using?

    I'm eager to find this ellusive node, it's just that I want to see if I can work it out algebraically so I know where to look.
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  3. #3
    Super Member Deadstar's Avatar
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    Ok. Its a saddle-node bifurcation and there's also another picture that im supposed to find the node on...

    Here's the equation u'(t) = -au + v, v'(t) = \frac{1}{1+u^2} - v

    But iv'e found the node in that picture i posted. You have to extend the axis and its there.

    But my next problem is to find the node when a is negative. Its only there between -0.1 and 0 according to eigenvalues but i cant see it.

    a is set to -0.09 in this pic. The saddles way put to the left past -5. But wheres the node!
    Attached Thumbnails Attached Thumbnails Saddles and Nodes-0.09.jpeg  
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