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arXiv · 2406.14224

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

Divya D. Joshi·Prashant M. Gade
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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 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 $i 2$. For $n=2$, a different exponent is observed.

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Divya D. Joshi, Prashant M. Gade. 2024-06-20. Cellular Automata model for period-$n$ synchronization: A new universality class. https://arxiv.org/abs/2406.14224

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