Analysis of various transient phenomena and co-existing periodic spike-trains in simple digital spike maps

This paper studies various transient- and steady-state spike-trains generated by the digital spike map: a simple digital dynamical system from a set of one-dimensional lattice points to itself. In order to consider the spike-trains, three feature quantities are presented: 1) the number of periodic spike-trains that can characterize richness of the steady states, 2) the concentricity of spike-position transition that can characterize transition of map, and 3) the concentricity of direct transition to the periodic spike-trains that can characterize local stability of the steady state. Based on these quantities, we give basic classification of dynamics of spike-trains and demonstrate typical examples. The results can be basic information to develop study of digital spike systems and their applications.