We introduce a voltage-gated conductance model for an artificial neuron that exhibits tonic, fast, and two types of intrinsic burst spiking. The spike generation is achieved with a single voltage-gated channel that exploits the conductance commutation properties of a two-terminal memristive device. Our circuit implementation is of unprecedented simplicity, using just four electronic components, all conventional, cheap and out-of-the-shelf. Our bursting neuron is a two-compartment model, similar to the Pinsky–Rinzel model. We obtain the full phase diagram and discuss the origin of the different regions. We find that the spike traces of the model bare striking similarity to experimental biological neuronal recordings. Our work may open a new way to investigate neural pathologies, such as epilepsy and Parkinson’s disease, from the study of the phase diagram and the transitions between spiking states of physical neuron models.