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

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 seldom observed. Recently a transition to a synchronized period-3 state that is not in DP class is observed. We model it 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 value of either neighbor 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.