Exercise 3. (Pitchfork bifurcation)For each of the following equations sketch all the qualitatively different vector fields and find all fixed points and their stability as the parameter r is varied,...

Extracted text: Exercise 3. (Pitchfork bifurcation)For each of the following equations sketch all the qualitatively different vector fields and find all fixed points and their stability as the parameter r is varied, determine the critical value r. at which the pitchfork bifurcation happens and if it is subcritical or supercritical, and sketch the bifurcation diagram. • i = rx +4x3 • i = rx - 4x³ • i = rx – sinh x %3D • i = x+ 1+x² 1,