Dynamical phase transitions in graph cellular automata
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489457" target="_blank" >RIV/00216208:11320/24:10489457 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xMR-wSPvy~" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xMR-wSPvy~</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevE.109.044312" target="_blank" >10.1103/PhysRevE.109.044312</a>
Alternative languages
Result language
angličtina
Original language name
Dynamical phase transitions in graph cellular automata
Original language description
Discrete dynamical systems can exhibit complex behavior from the iterative application of straightforward local rules. A famous class of examples comes from cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we relax the regular connectivity grid of cellular automata to a random graph, which gives the class of graph cellular automata. Using the dynamical cavity method and its backtracking version, we show that this relaxation allows us to derive asymptotically exact analytical results on the global dynamics of these systems on sparse random graphs. Concretely, we showcase the results on a specific subclass of graph cellular automata with "conforming nonconformist" update rules, which exhibit dynamics akin to opinion formation. Such rules update a node's state according to the majority within their own neighborhood. In cases where the majority leads only by a small margin over the minority, nodes may exhibit nonconformist behavior. Instead of following the majority, they either maintain their own state, switch it, or follow the minority. For configurations with different initial biases towards one state we identify sharp dynamical phase transitions in terms of the convergence speed and attractor types. From the perspective of opinion dynamics this answers when consensus will emerge and when two opinions coexist almost indefinitely.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physical Review E
ISSN
2470-0045
e-ISSN
2470-0053
Volume of the periodical
109
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
044312
UT code for WoS article
001226393400001
EID of the result in the Scopus database
2-s2.0-85190826180