Exercise 2. (Transcritical bifurcation)For each of the following equations sketch all the qualitatively different vector fields and find all fixed points and their sta- bility as the parameter r is...

Extracted text: Exercise 2. (Transcritical bifurcation)For each of the following equations sketch all the qualitatively different vector fields and find all fixed points and their sta- bility as the parameter r is varied, determine the critical value re at which the transcritical bifurcation happens, and sketch the bifurcation diagram. • i = rx+x² • i = rx – In (1+x) • i = 1- rI(1 1) - ra(1– • i = x(r - e)