Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing pattes are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing patte lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.