Transitions of different neuronal firing patterns in the Chay model are explored by numerical simulation of three firing sequences observed in experiments on neural pacemakers, and the bifurcation analysis of limit cycle. Firstly,the transitions of periodic firing patterns through a pair of period-doubling bifurcations are obtained. Secondly,a supercritical and a subcritical period-doubling bursting sequences with different appearances lead to chaos,and then transit to an inverse period-doubling spiking sequence in different ways,separately. Finally,we reveal the true nature of period-adding bursting sequence without chaotic bursting,which is closely related to period-doubling bifurcation.