Consider the family of ODE's: @ = r + 2 - -& , PER

Consider the family of ODE's: @ = r + 2 - -& , PER. (A) Sketch three vector fields for r = 0, r large and positive, r large and negative, identifying the stability of the fixed points. (B) Find all the bifurcation(s) that occur as " is varied, and determine the bifurcation point(s) (@*, r) exactly. (C) Sketch the bifurcation diagram and identify the type of bifurcation(s) occurring (D) Suppose r starts at r = -2 and is slowly increased to r = 2, and then decreased slowly back to r = -2. Sketch on the bifurcation diagram the evolution of a solution near the equilibrium solution during this procedure.