A detailed bifurcation analysis of heat integrated homogeneous tubular reactors is presented. The analysis is based on a one-dimensional discrete map obtained from the PDE model by means of the method of characteristics. It is shown that, under operating conditions in which the heat integration provides a positive feedback mechanism, the reactor may destabilize through a saddle-node bifurcation, resulting in multiple steady states. Under conditions in which the heat integration provides a negative feedback mechanism, the reactor may destabilize through a flip bifurcation, resulting in periodic solutions. It is shown that these periodic solutions subsequently may undergo a cascade of period doubling bifurcations into chaos. The period doubling cascade is found to follow the proposed universal Feigenbaum scenario. Higher periodic solutions and chaos is found to exist in a relatively large area of parameter space.