/sci/ - Science & Math

Why does a high growth rate diminishes the carrying capacity?

I'm plotting the simple function [math]\frac{\mathrm{d}x}{\mathrm{d}t} = rx(1-x)[/math], with initial condition of 0<x<1. Why does my asymptote gets lower and lower as my growth rates gets higher than 2.74?

Also, why doesn't bifurcation happen on continuous time domain?