# A Bifurcation Diagram in AUTO

1. Apr 6, 2017

### joshmccraney

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:

• ###### bifurcation.pdf
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Last edited: Apr 6, 2017
2. Apr 6, 2017

### 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.

3. Apr 6, 2017

### joshmccraney

I'm happy to, but I don't know how to do this?

4. Apr 6, 2017