Rich spike-synchronization phenomena of pulse-coupled bifurcating neurons

This paper studies the spike-synchronization phenomena of pulse-coupled bifurcating neuron circuits. Each neuron includes one capacitor and its voltage exhibits integrate-and-fire behavior between a firing threshold and a periodic base signal. It can output rich spike-trains. The pulse-coupling is realized by interaction of the integrate-and-fire behavior of two neurons. As a theoretical result we provide a condition for the existence of fundamental chaotic and periodic synchronizations. Since the system is piecewise linear, precise numerical analysis is possible and we can demonstrate rich spike-synchronous phenomena.