Firing patterns and complete synchronization of coupled Hindmarsh–Rose neurons

The firing activities of Hindmarsh–Rose (HR) neurons are studied by means of numerical simulation and bifurcation analysis. A single HR neuron exhibits various firing patterns, such as quiescent state, periodic spiking, periodic bursting and chaos, when the external current input is changed. The fast/slow dynamical analysis is applied to explore the dynamical behaviour of the HR model. The complete synchronization of two coupled identical HR neurons with electrical coupling mimicking gap junctions can be realized in certain ranges of the coupling strength, whenever each individual neuron shows quiescency, periodic firing and chaos. The criteria for complete synchronization are analysed theoretically and the corresponding numerical simulation is presented as well. The persistence of the interspike intervals bifurcation structure of the coupled HR neuronal system under electrical coupling is also discussed.