Bifurcation in mutually coupled three neurons with inhibitory synapses

We investigate a system of mutually coupled three neurons in a line with the inhibitory synapses as a basic motif of complex networks. For class I and class II neurons, bifurcation structure is analyzed when we change the external DC current of a middle neuron. In both classes, the neurons have a wide parameter region in which stable 1:2 cluster synchronous firing is observed as the external DC current of a middle neuron becomes larger than that of outer neurons. For only class I neurons, we observe the stable non-in-phase synchronous firing between three neurons.