Static and dynamic bifurcation behaviors dominate the operation of fluidized bed catalytic reactors for the production of polyethylene (UNIPOL Process) and have important implications on the safe operating temperature and polyethylene production rate. The investigations show that the multiplicity of the steady state phenomenon covers a wide range of parameters together with the phenomenon of periodic oscillations with sharply changing amplitudes with a change of the chosen bifurcation parameter. In some cases, the periodic branches terminate through periodic limit point (PLPs), while in other cases it terminates homoclinically. A detailed parameteric investigation using two-parameter continuation diagrams for the loci of static and Hopf bifurcation points as well as one parameter bifurcation diagrams shows that it is possible to increase the productivity of the unit considerably without exceeding the constraints of the polymer melting point. Gas feed temperature, catalyst feed rate, and polymer particle size distribution are important operating parameters in polyethylene fluidized bed reactors. Gas velocity plays a significant role in keeping the fluidized bed bubbling in addition to the fact that it acts as a cooling media by removing excess heat generated from the polymerization reaction. The kinetic behavior of the catalyst and effect of reactor temperature on product properties require, in some cases, operating just below the softening point of the polymer which requires a suitable controller to avoid polymer melting.