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Reviews of topical problems


Study of spatially extended dynamical systems using probabilistic cellular automata


Photochemistry Center, Russian Academy of Sciences, Novatorov str. 7a, Moscow, 117421, Russian Federation

Spatially extended dynamical systems are ubiquitous and include such things as insect and animal populations; complex chemical, technological, and geochemical processes; humanity itself, and much more. It is clearly desirable to have a certain universal tool with which the highly complex behaviour of nonlinear dynamical systems can be analyzed and modelled. For this purpose, cellular automata seem to be good candidates. In the present review, emphasis is placed on the possibilities that various types of probabilistic cellular automata (PCA), such as DSMC (direct simulation Monte Carlo) and LGCA (lattice-gas cellular automata), offer. The methods are primarily designed for modelling spatially extended dynamical systems with inner fluctuations accounted for. For the Willamowskii-Roessler and Oregonator models, PCA applications to the following problems are illustrated: the effect of fluctuations on the dynamics of nonlinear systems; Turing structure formation; the effect of hydrodynamic modes on the behaviour of nonlinear chemical systems (stirring effects); bifurcation changes in the dynamical regimes of complex systems with restricted geometry or low spatial dimension; and the description of chemical systems in microemulsions.

Fulltext pdf (891 KB)
Fulltext is also available at DOI: 10.1070/PU1999v042n05ABEH000558
PACS: 02.50.Ng, 02.70.Lq, 05.70.Ln, 87.10.+e (all)
DOI: 10.1070/PU1999v042n05ABEH000558
URL: https://ufn.ru/en/articles/1999/5/a/
000080958700001
Citation: Vanag V K "Study of spatially extended dynamical systems using probabilistic cellular automata" Phys. Usp. 42 413–434 (1999)
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Оригинал: Ванаг В К «Исследование пространственно распределенных динамических систем методами вероятностного клеточного автомата» УФН 169 481–505 (1999); DOI: 10.3367/UFNr.0169.199905a.0481

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  1. Bashabsheh M Int. J. Math. Eng. Manag. Sci. 10 (2) 522 (2025)
  2. Mapelli C, Dall’Osto Gianluca et al Steel Research Int. 95 (3) (2024)
  3. Bhasin D, Karmakar S et al Electron. J. Probab. 28 (none) (2023)
  4. Medvedev Yu, Kireev S, Trubitsyna Yu Lecture Notes In Computer Science Vol. Parallel Computing TechnologiesExpanding the Cellular Automata Topologies Library for Parallel Implementation of Synchronous Cellular Automata14098 Chapter 8 (2023) p. 93
  5. Ghaemi M, Shojafar M et al PLoS ONE 17 (3) e0265065 (2022)
  6. Fedchenko D P, Novikov V V, Timofeev I V J. Phys.: Conf. Ser. 2094 (2) 022079 (2021)
  7. (THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019) Vol. THE 2ND INTERNATIONAL CONFERENCE ON PHYSICAL INSTRUMENTATION AND ADVANCED MATERIALS 2019Fractal models in analysis of energy transfer processes at intermolecular interactionA. A.BaratovaK. S.Baktybekov2314 (2020) p. 030038
  8. Manneville P, Shimizu M Entropy 22 (12) 1348 (2020)
  9. Menshutina N V, Kolnoochenko A V, Lebedev E A Annu. Rev. Chem. Biomol. Eng. 11 (1) 87 (2020)
  10. Gorodnichev M, Medvedev Yu Lecture Notes In Computer Science Vol. Parallel Computing TechnologiesA Web-Based Platform for Interactive Parameter Study of Large-Scale Lattice Gas Automata11657 Chapter 25 (2019) p. 321
  11. Štys Dalibor, Rychtáriková R et al Eur. Phys. J. Spec. Top. 227 (15-16) 2361 (2019)
  12. Kislyuk V, Melnyk A et al Journal of Electrical Engineering 70 (7) 83 (2019)
  13. Bandman O L Numer. Analys. Appl. 11 (1) 4 (2018)
  14. Rezvanov A A, Matyushkin I V et al Russ Microelectron 47 (6) 415 (2018)
  15. Hu Yu, Xie Je AIP Advances 8 (12) (2018)
  16. Gavrilov S V, Matyushkin I V, Stempkovsky A L Sci. Tech. Inf. Proc. 44 (5) 314 (2017)
  17. Vertyagina Y, Marrow T Ja Carbon 121 574 (2017)
  18. Gurikov P, Kolnoochenko A et al Computers & Chemical Engineering 84 446 (2016)
  19. Bandman O L, Kireeva A E Numer. Analys. Appl. 8 (3) 208 (2015)
  20. Chumak O V Plasma Phys. Rep. 39 (8) 651 (2013)
  21. Dziekan P, Lemarchand A, Nowakowski B The Journal of Chemical Physics 137 (7) (2012)
  22. Vanag V K Russ J Gen Chem 81 (1) 181 (2011)
  23. Ghaemi M, Naderi O, Zabihinpour Z Lecture Notes In Computer Science Vol. Cellular AutomataA Novel Method for Simulating Cancer Growth6350 Chapter 15 (2010) p. 142
  24. Mozhaev A V, Prokaznikov A V Russ Microelectron 38 (5) 291 (2009)
  25. Rohlf K J Math Chem 45 (1) 141 (2009)
  26. Mozhaev A V, Buchin E Yu, Prokaznikov A V Tech. Phys. 54 (3) 327 (2009)
  27. Mozhaev A V, Buchin ω Yu, Prokaznikov A V Tech. Phys. Lett. 34 (5) 431 (2008)
  28. Vanag V K, Epstein I R Springer Series In Materials Science Vol. Self-Organized Morphology in Nanostructured MaterialsPatterns of Nanodroplets: The Belousov-Zhabotinsky-Aerosol OT-Microemulsion System99 Chapter 5 (2008) p. 89
  29. Agafonov A N, Agaphonov A N i dr Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-matematicheskie Nauki 1(14) 99 (2007)
  30. Alekseev D V, Kazunina G A J Min Sci 42 (1) 43 (2006)
  31. Alekseev D V, Kazunina G A Phys. Solid State 48 (2) 272 (2006)
  32. Karstina S G, Baktybekov K S, Vertyagina E N Russ Phys J 48 (6) 553 (2005)
  33. Kaplii S A, Prokaznikov A V, Rud N A Tech. Phys. 50 (12) 1535 (2005)
  34. Stetsyura G G Automation And Remote Control 65 (8) 1328 (2004)
  35. Kapliy S A, Prokaznikov A V, Rud’ N A Tech. Phys. Lett. 30 (7) 595 (2004)
  36. Bykov V I, Tatarenko A A, Slin’ko M G Doklady Physical Chemistry 392 (4-6) 264 (2003)
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