Interaction function of coupled bursting neurons

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.