A two-cell model with backflow and heat exchange is developed to analyze the dynamics of an LDPE compact autoclave reactor. The backflow exists between the two mixing cells and represents the degree of mixing within the reactor. The performance of the reactor and the physical properties of the product polymer such as the number average molecular weight and the polydispersity are investigated under various operating conditions, especially when the initiator feed concentration is varied. Bifurcation diagrams are constructed by taking the initiator feed concentration as the bifurcation parameter and the dynamic feature in the feasible parameter ranges for operation are carefully examined. Indeed, various dynamic characteristics are observed by performing numerical analysis of the nonadiabatic system with the internal cooling device. As the rate of heat transfer increases, various multiplicity patterns and oscillatory behavior such as the limit cycle and the focus are found. The reactor behavior even undergoes period doubling and gradually gives rise to a chaotic behavior in certain ranges of the initiator feed concentration when the coolant temperature becomes low. The existence of chaos is examined by the phase plane plot and Poincare: map. Apparently, the monomer concentration can be substantially increased with proper heat removal and initiator supplement scheme. For this, however, the complex dynamic features must be taken into account in the reactor design.