Bifurcation phenomena of simple pulse-coupled spiking neuron models with filtered base signal

This paper studies nonlinear phenomena of pulse-coupled bifurcating neurons. Repeating integrate-and-fire dynamics between a constant threshold and periodic base signal, the bifurcating neuron outputs a spike-train. Applying a low-pass filter to the periodic square wave, we obtain the base signal. As parameters of the filter vary, the shape of the base signal varies and the neurons can exhibit a variety of periodic/chaotic spike-trains and related bifurcation phenomena. We consider typical phenomena. First, the single bifurcating neuron can exhibit the period doubling bifurcation where both period and the number of spike-trains are doubling. Second, the pulse-coupled two bifurcating neurons can exhibit the tangent bifurcation that causes “chaos + chaos = order”: chaotic spiketrains of two single neurons are changed into periodic spiketrain by the pulse-coupling. Such phenomena are filter-induced bifurcations because they are caused by the filtering. The bifurcation sets are calculated precisely based on the state equation of the filter and the one-dimensional spike-phase map. Presenting a simple test circuit, typical phenomena are confirmed experimentally.