The interaction functions of electrically coupled Hindmarsh–Rose（HR） neurons for different firing patterns are investigated in this paper.By applying the phase reduction technique,the phase response curve（PRC） of the spiking neuron and burst phase response curve（BPRC） of the bursting neuron are derived.Then the interaction function of two coupled neurons can be calculated numerically according to the PRC（or BPRC） and the voltage time course of the neurons.Results show that the BPRC is more and more complicated with the increase of the spike number within a burst,and the curve of the interaction function oscillates more and more frequently with it.However,two certain things are unchanged：Φ = 0,which corresponds to the in-phase synchronization state,is always the stable equilibrium,while the anti-phase synchronization state with Φ = 0.5 is an unstable equilibrium.
The spatiotemporal order and rhythm dynamics of a complex neuronal network with mixed bursting neurons are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neuronal network. An r parameter is introduced to denote the ratio of the short bursting neurons in the network. Then we investigate the effect of the ratio on the rhythm dynamics of the neuronal network. The critical value of r is derived, and the neurons in the network always remain short bursting when the r ratio is larger than the critical value.
