Phase response properties of a bursting neuron with spike adding structure

The phase response properties of the Hindmarsh-Rose model in different blocks are investigated in this paper. We find: (1) the location of the largest magnitude of the BPRCs can only be in the penultimate spike or the final spike which depends on the position of the system in the block. (2) the location of the largest magnitude of the BPRCs changes sharply when the system transits from one block to the neighbor one. Then we use bifurcation diagrams of fast subsystem with the slow variable as the bifurcation parameter to analyze the structure of the BPRCs, and draw the conclusions that the slow variable is critical in determining the properties of BPRCs, especially the location of the largest magnitude of the BPRCs, which depends on the difference between the values of slow variable for the spike maxima and for the homoclinic bifurcation.