Creating function from jacbian maxima

Question

I want to use Maxima to do linear stability analysis as function of r:

f(x):=rx + x^3 - x^5
A:solve(f(x)=0,x)
J:jacobian([f(x)],[x])

Now for each element in A, I want to check the sign of J as a function of r. In general I want a function from r that gives that tells me if there exists any eigenvalue to J with positive real part.

Answer 1

Maybe you know this already, but: multiplication in Maxima is indicated by an asterisk. So you have to write:

f(x):=r*x + x^3 - x^5;

I don't see any problem with your approach so far. The Jacobian is a 1 by 1 matrix so it is trivial to compute the eigenvalue. Then substitute values of x into that, and look at the real part (function realpart).