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Pattern dynamics in the Belousov-Zhabotinsky coupled map lattice

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Abstract

The Dynamics of the Belousov-Zhabotinsky (BZ) coupled map lattice (CML) was studied as a model of spatiotemporal pattern. The systematical change of coupling strength and bifurcation parameter led to the shifts in the patterns of the BZ CML. The phase diagram of the BZ CML was different from that of the logistic CML. The phases, such as fully developed turbulence, pattern competition intermittency and pattern selection observed in the logistic CML, appeared in the BZ CML. However, the dynamics of the BZ CML were more sensitive to the coupling strength than those of the logistic CML. In addition, the periodic oscillation phase was observed as small a number of patterns without the domain of chaotic motion. Furthermore, we discussed the difference between the BZ and the logistic CML on the basis of intermittency of chaos.

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References

  1. K Kaneko Physica D 34 1 (1989)

  2. K Kaneko Physica D 41 137 (1990)

  3. K Kaneko Theory and Applications of Coupled Map Lattices (New York: Wiley) (1993)

  4. S Kinoshita Pattern Formations and Oscillatory Phenomena (Boston: Elsevier) (2013)

  5. S K Scott Chemical Chaos (UK: Oxford University Press) (1994)

  6. A T Winfree The Geometry of Biological Time (New York: Springer-Verlag) (2001)

  7. H Zhang and D Liu Z Wang Controlling Chaos: Suppression, Synchronization and Chaotification. (New York: Springer-Verlag)) (2009)

    Book  Google Scholar 

  8. Y Kuramoto Chemical Oscillations, Waves, and Turbulence (New York: Dover Publications) (1984)

  9. A Adamatzky Identification of Cellular Automata (London: Taylor and Francis) (1994)

  10. H V McIntosh One Dimensional Cellular Automata (UK: Luniver Press) (2009)

  11. A Wuensche M Lesser The Global Dynamics of Cellular Automata. (Addison-Wesley): Santa Fe) (1992)

    MATH  Google Scholar 

  12. A Deutsch S Dormann Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis. (Boston: Birkhäuser)) (2005)

    Google Scholar 

  13. W Fitzgibbon, Y A Kuznetsov, P Neittaanmaeki and J Périaux O Pironneau Applied and Numerical Partial Differential Equations. (Netherlands: Springer-Verlag)) (2010)

    Book  Google Scholar 

  14. J Jost Partial Differential Equations (New York: Springer-Verlag) (2013)

  15. H Yizhaq and G Bel New J. Phys. 18 023004 (2016)

    Article  ADS  Google Scholar 

  16. J R Chazottes B Fernandez Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems. (Berlin Heidelberg: Springer-Verlag)) (2005)

    Book  Google Scholar 

  17. A M dos Santos, R L Viana, S R Lopes, S E de Pinto and A M Batista Physica A 387 1655 (2008)

    Article  ADS  Google Scholar 

  18. V Garcia-Morales J. Phys. A 49 295101 (2016)

  19. S Strogatz SYNC: The Emerging Science of Spontaneous Order (New York: Hyperion Press) (2003)

  20. R J Field and E Körös R M Noyes J. Am. Chem. Soc. 94 8649 (1972)

    Article  Google Scholar 

  21. L Györgyi and R J Field Nature 355 808 (1993)

    Article  ADS  Google Scholar 

  22. M Yoshimoto and J Katsura J. Phys. Soc. Jpn. 71 1875 (2002)

    Article  ADS  Google Scholar 

  23. T Killingback, G Loftus and B Sundaram Phys. Rev. E 87 022902 (2013)

    Article  ADS  Google Scholar 

  24. M Sano and Y Sawada Phys. Rev. Lett. 55 1082 (1985)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Information Science and Biomedical Engineering, Graduate School of Science and Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima, 890-0065, Japan

    Minoru Yoshimoto

  2. Health and Medical Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Central 6, 1-1-1 Higashi, Tsukuba, Ibaraki, 305-8566, Japan

    Shigeru Kurosawa

Authors
  1. Minoru Yoshimoto
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  2. Shigeru Kurosawa
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Correspondence to Minoru Yoshimoto.

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Yoshimoto, M., Kurosawa, S. Pattern dynamics in the Belousov-Zhabotinsky coupled map lattice. Indian J Phys 96, 1489–1500 (2022). https://doi.org/10.1007/s12648-021-02074-5

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