I am trying to plot the bifurcation diagram based on the steady-state values of the following ODE:
$$\frac{dx}{dt}=x(1-x)-rx$$
I take the right hand side $f(x) = x(1-x)-rx$ and I find the fixed points of $g(x) = f(x)+x$ which will give me the zeros of $f(x)$ hence the steady state points of the ODE.
I find the fixed points of $g(x)$ using the method introduce in here and by the recursive relationship $x_{n+1}=g(x_n)$.
I get the following diagram:
As you can see I am getting negative values. But this is a population growth model and shouldn't be negative. In fact, I give values of r>3 to the ODE and the dynamics go to zero but never negative. I very much appreciate it if you can help me with this.