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A Bifurcation Diagram in AUTO

  1. Apr 6, 2017 #1

    joshmccraney

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    Gold Member

    Hi PF

    I am given the ODE ##\ddot{\theta} +q\sin\theta+\mu\cos\theta=0##, where I introduce ##x_1 = \theta## and ##x_2=\dot{\theta}## to yield$$
    \dot{x_2}=-q\sin x_1-\mu\cos x_1\\
    x_2=\dot{x_1}
    $$
    subject to ##x_2(0)=x_2(1)=0## and ##\int_0^1\sin x_1\, d t = 0##. I then plug this system into the program AUTO, a bifurcation detection software. The bifurcation plot is attached. My question is, what does this graph represent mathematically? What would the value of one point, say 17, represent?

    Thanks a ton for your help!
     

    Attached Files:

    Last edited: Apr 6, 2017
  2. jcsd
  3. Apr 6, 2017 #2

    jedishrfu

    Staff: Mentor

    Can you post the graph directly as an image instead of a pdf? Not everyones browser opens pdf files especially with the issues Adobe has with malware.
     
  4. Apr 6, 2017 #3

    joshmccraney

    User Avatar
    Gold Member

    I'm happy to, but I don't know how to do this?
     
  5. Apr 6, 2017 #4
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