Analysis of digital spike maps based on bifurcating neurons

Abstract

This paper studies digital spike maps that can generate various periodic spike-trains. In order to analyze the dynamics, we consider two measures that are basic to characterize the number of periodic spike-trains and their domain of attraction. As a typical example, we consider a map based on discretized bifurcating neurons. Applying a simple calculation algorithm, we can show that the map can exhibit rich periodic spike-trains as a parameter vary.