linear stability analysis of ODE

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Tanja Gesslbauer
Tanja Gesslbauer 2017-6-17
评论： Sagar Doshi 2017-6-20
Hello there!
I have a question regarding linear stability analysis in MatLab.
given is the ODE
x' = x - x^3
of which I have calculated the fixed points x1 = 0 x2 = 1 x3 = -1
Now these points have to be checked for stability, both graphically and by means of linear stability analysis. I started doing that, by doing a linearization of the given differential equation and trying to set up a Jacobian.
But: since I've only got one variable and one equation, the Jacobian is reduced to a skalar, or am I seeing this wrong?
I'd need the Jacobian to get the eigenvalues and further the stability, so I can plot it in MatLab, but I don't see how I could do it with this equation.
So I would really be grateful for some help. Greetings, Tanja :-)
  1 个评论
Sagar Doshi
Sagar Doshi 2017-6-20
You are correct about the Jacobian for single equation with one variable is a scalar. This can also be seen in the Wikipedia link for liner stability here .

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