Cellular automata model for period-n synchronization: a new universality class

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.