Periodic orbit analysis for the deterministic path-preference traffic flow cellular automaton

The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we propose an exact analysis for the simplest version of this model. We find that the number of particles is dominant to the dynamics of this cellular automaton and observed that there are not only expected phase shift but also several gaps as the number of particles increases. By considering the behavior of periodic orbits, we also determine the point where such gaps in the flow appear and the exact value of the flow.