For each of the following exercises, sketch all the qualitatively different vector fields that occur as r is varied. Show that a transcritical bifurcation occurs at a critical value of r, to be determined. Finally, sketch the bifurcation diagram of fixed points x* vs. r. 3.2.1 3.2.3 x=rx+x² x=x-rx(1-x) 3.2.2 3.2.4 x=rx-ln(1+x) x = x(r-e*)