Pulse replications and spatially differentiated structure formation in one-dimensional lattice dynamical system

Replication and differentiation of pulses are studied through a simple dynamical system on a one-dimensional lattice. Depending on the parameter values, our proposed system exhibits the following types of pulse replications: (I) each pulse replicates by itself, (II) each pulse replicates if two or more pulses collide each other, and (III) pulses replicate by the organization of pulse generators. Moreover, replicated pulses construct the spatial–temporal pattern when the number of pulses is large. By selecting local objects in such spatial–temporal patterns and replanting them numerically, it is found that there are two types differentiated local structures: one that continues the production of pulses and the other that does not.