Cellular Automata model for period-$n$ synchronization: A new universality class

TL;DR

This paper introduces a cellular automata model for period-$n$ synchronization transitions, revealing a new universality class with distinct critical exponents from directed percolation, especially for $n>2$.

Contribution

It proposes a novel cellular automata framework for studying periodic synchronization transitions, identifying a new universality class with unique critical behavior.

Findings

Transition to synchronization with distinct critical exponents for $n>2$

Different critical exponents observed for $n=2$

Model captures universality class beyond directed percolation

Abstract

There are few known universality classes of absorbing phase transitions in one dimension and most models fall in the well-known directed percolation (DP) class. Synchronization is a transition to an absorbing state and this transition is often DP class. With local coupling, the transition is often to a fixed point state. Transitions to a periodic synchronized state are possible. We model those using a cellular automata model with states 1 to $n$. The rules are a) Each site in state $i$ changes to state $i+1$ for $i<n$ and 1 if $i=n$. b) After this update, it takes the value of either neighbour unless it is in state 1. With these rules, we observe a transition to synchronization with critical exponents different from those of DP for $n>2$. For $n=2$, a different exponent is observed.