Exercise 1. (Saddle-Node 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 1. (Saddle-Node 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 r. at which the saddle-node bifurcation happens, and sketch the bifurcation diagram. • i = 1+rx + x² • i =r+x – In (1+x) • i =r – cosh x • i = r+x - 1+x