Rich dynamics of pulse-coupled spiking neurons with a triangular base signal

This paper presents a spiking neuron circuit with a triangular base signal. The circuit can output rich pulse-trains and the dynamics can be analyzed using a piecewise linear one-dimensional pulse-position map. Applying cross-switching to two neurons we construct a pulse-coupled system whose dynamics can be integrated into a composite map of the pulse position maps of two neurons. The composite map is piecewise linear and precise analysis is possible. We can clarify various interesting phenomena caused by the pulse-coupling. For example, periodic behavior of each neuron is changed into chaotic behavior and chaotic behavior of each neuron is changed into periodic behavior. These results provide basic information to construct flexible pulse-coupled neural networks.