How plot a bifurcation diagram ? or show find bifurcation points

Question

I have a function $rx(3-x^2)$

How do I find the points it bifurcates and what does it mean ?

I know how to find fixed points and check them for stability, how can I use that to answer this question ?

Answer 1

Answer to first question (in case where x is a 1D variable ):

How plot a bifurcation diagram ?

1. for r from $r_{min}$ to $r_{max}$ compute $i_{max}$ iterations : $x_{i+1} = f_r(x_i) = rx_i(3-x_i^2)$. Then you have a list of 2D points : [r,x], so you can plot it on the 2D diagram with r on horizontal axis and x on vertical one.
2. Make new diagram : try to clear diagram by removing preperiodic points = first make some iterations without drawing it, then make more iterations and draw each point

More is here ( images , code )

HTH