The chaotic behaviour of the fluidized-bed catalytic reactor with exothermic consecutive reactions is investigated for the case where the dynamics of the product is very fast and the feed temperature is periodically forced. The investigation concentrates on the less studied case when the centre of forcing is close to the homoclinical orbit of the autonomous system and preliminary results for the effect of the distance between the centre of forcing and the homoclinical orbit are presented. It is shown that period doubling and chaos occur for very small amplitudes of forcing when the centre of forcing is close to the homoclinical orbit. A new type of intermittency with two laminar phases of different periodicities has been uncovered and analysed. The mechanisms for the transition between chaotic regions and periodic windows have been identified and they include period doubling, period halving, period adding and tangent bifurcation. It has been shown that some chaotic regions separate windows which are different in periodicity by one period (period adding), while other chaotic regions separate windows having the same periodicity. The system exhibited one-dimensional stroboscopic maps which resemble a number of the well-known maps of simpler systems.