3. (30 points) Consider the system x=rx+hx2x3 (a) Find the fixed points of this system analytically. Based on these results, determine the equation for the bifurcation curve(s) h=hc(r). (b) Consider the case h>0. Sketch x3hx2 and rx, as r varies. How many fixed points are there? Does the answer depend on the value of r ? If so, list the different cases. (c) Consider the case h0. Sketch x3hx2 and rx, as r varies. How many fixed points are there? Does the answer depend on the value of r ? If so, list the different cases. (c) Consider the case h