Firing rhythm patterns and the interspike intervals (ISIs) bifurcation structures of the action potential in the modified Morris-Lecar (ML) neuronal model are investigated.By modulating two important control parameters μand Vk,we find that for some fixed μ,varying Vk,the neuron exhibits a cascade of period doubling bifurcation and period-adding bifurcation leading the system from the silent regime to a periodic and chaotic state dominated by bursting events; While,if we take some peculiar values of Vk based on the former bifurcation diagram,modulating μcan lead to a variety of bifurcation structures which have something to do with the single neuron’s firing patterns,moreover,chaotic bursting brings us much richer bifurcation dynamics than periodic bursting.We know that neurons can encode information by use of action potentials,based on this,we infer that study of firing rhythm patterns and ISIs structures can be a clue to understand the mechanism of the neuronal encoding.