Bifurcation theory and numerical continuation techniques are used to investigate the complex static and dynamic characteristics of a fixed-bed reactor modelled by a heterogeneous cell model. The model takes into account the thermal coupling between adjacent reactor cells due to radiation and conduction. A rich variety of interesting static phenomena is uncovered, including, multiplicity with a large number of steady states. A Hopf bifurcation point is identified from which a periodic branch emanates. The periodic branch terminates at a homoclinical infinite period (IP) bifurcation point. Wrong-way behaviour and sensitivity of the final steady-state profile to initial conditions are also observed.