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 t...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2025-01, Vol.58 (2), p.2
Main Authors: Joshi, Divya D, Gade, Prashant M
Format: Article
Language:English
Subjects:
absorbing phase transitions
cellular automata model
universality class
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Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ad9e58