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

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          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 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.

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          Journal
          20 June 2024
          Article
          2406.14224
          1c937cd1-fb79-48cb-85a4-40017a1c05f9

          http://creativecommons.org/licenses/by/4.0/

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          cond-mat.stat-mech

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