The neural mechanisms generating rhythmic bursting activity in the mammalian brainstem, particularly in the pre-Bötzinger complex (pre-BötC), which is involved in respiratory rhythm generation, and in the spinal cord (e.g. locomotor rhythmic activity) that persist after blockade of synaptic inhibition remain poorly understood. Experimental studies in rodent medullary slices containing the pre-BötC identified two mechanisms that could potentially contribute to the generation of rhythmic bursting: one based on the persistent Na+ current (INaP), and the other involving the voltage-gated Ca2+ current (ICa) and the Ca2+-activated nonspecific cation current (ICAN), activated by intracellular Ca2+ accumulated from extracellular and intracellular sources. However, the involvement and relative roles of these mechanisms in rhythmic bursting are still under debate. In this theoretical/modelling study, we investigated Na+-dependent and Ca2+-dependent bursting generated in single cells and heterogeneous populations of synaptically interconnected excitatory neurons with INaP and ICa randomly distributed within populations. We analysed the possible roles of network connections, ionotropic and metabotropic synaptic mechanisms, intracellular Ca2+ release, and the Na+/K+ pump in rhythmic bursting generated under different conditions. We show that a heterogeneous population of excitatory neurons can operate in different oscillatory regimes with bursting dependent on INaP and/or ICAN, or independent of both. We demonstrate that the operating bursting mechanism may depend on neuronal excitation, synaptic interactions within the network, and the relative expression of particular ionic currents. The existence of multiple oscillatory regimes and their state dependence demonstrated in our models may explain different rhythmic activities observed in the pre-BötC and other brainstem/spinal cord circuits under different experimental conditions.