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Fractal patterns on the onset of coherent structures in a coupled map lattice

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Abstract

We report the formation of Cantor set-like fractals during the development of coherent structures in a coupled map lattice (CML). The dependence of these structures on the size of the lattice as well as the first three dimensions of the associated fractal patterns are analyzed numerically.

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References

  1. A R Bishop, G Gruner and B Nicolaenko (eds) Physica D23 (1986)

  2. K Kaneko, Physica D41, 137 (1990)

    ADS  Google Scholar 

  3. G Perez, S Sinha and H A Cerdeira, Physica D63, 341 (1993)

    ADS  Google Scholar 

  4. K Kaneko, Theory and applications of coupled map lattices (Wiley, NY, 1993)

    MATH  Google Scholar 

  5. C Beck, Phys. Rev. E49, 3641 (1994)

    ADS  MathSciNet  Google Scholar 

  6. K Kaneko, Physica D37, 60 (1989)

    ADS  Google Scholar 

  7. Y Yanagita and K Kaneko, Phys. Lett. A175, 415 (1993)

    ADS  Google Scholar 

  8. F H Willeboordse and K Kaneko, Physica D86, 428 (1995)

    MathSciNet  Google Scholar 

  9. G Veser, F Mertens, A S Mikhailov and R Imbihl, Phys. Rev. Lett. 71, 935 (1993)

    Article  ADS  Google Scholar 

  10. R Kapral, R Livi, G L Oppo and A Politi, Phys. Rev. E49, 2009 (1994)

    ADS  MathSciNet  Google Scholar 

  11. H Meinhardt, Models of biological pattern formation (Academic, NY, 1982)

    Google Scholar 

  12. M P Hassell, O Miramontes, P Rohani and R M May, J Animal Eco. 64, 662 (1995)

    Article  Google Scholar 

  13. R V Sole and J Bascompte, J. Theor. Biol. 175, 139 (1995)

    Article  Google Scholar 

  14. K Kaneko, Physica D55, 368 (1992)

    ADS  Google Scholar 

  15. K Kaneko, Physica D54, 5 (1992)

    ADS  Google Scholar 

  16. K Ikede, K Otsuka and K Matsumoto, Prog. Theor. Phys. Suppl. 99, 195 (1989)

    Google Scholar 

  17. P Parmananda and Yu Jiang, Phys. Lett. A231, 159 (1997)

    ADS  MathSciNet  Google Scholar 

  18. S Parthasarathy and J Gue’mez, Ecological modelling 106, 17 (1998)

    Article  Google Scholar 

  19. F S de San Roman, S Boccalatti, D Maza and H Mancini, Phys. Rev. Lett. 81, 3639 (1998)

    Article  ADS  Google Scholar 

  20. W Wang and H A Cerdeira, Chaos 6(2), 200 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. R C Gonzalez, D K Arrowsmith and F Vivaldi, Phys. Rev. E61, 1329 (2000)

    ADS  Google Scholar 

  22. M Mehta and S Sinha, Chaos 10, 350 (2000)

    Article  MATH  ADS  Google Scholar 

  23. M B Ouchi and K Kaneko, Chaos 10, 350 (2000)

    Article  MathSciNet  Google Scholar 

  24. Paul Glendinning, Phys. Lett. A259, 129 (1999)

    ADS  MathSciNet  Google Scholar 

  25. Noriyuki Bob Ouchi and Kunihiko Kaneko, Chaos 10, 359 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Mitaxi Mehta and Sudeshna Sinha, Chaos 10, 350 (2000)

    Article  MATH  ADS  Google Scholar 

  27. Keiji Konishi, Hideki Kokame and Kentaro Hirata, Phys. Lett. A263, 307 (1999)

    ADS  Google Scholar 

  28. Yu Jiang, A Antillon and J Escalona, Phys. Lett. A262, 403 (1999)

    ADS  MathSciNet  Google Scholar 

  29. R E Amritkar and P M Gada, Phys. Rev. Lett. 70, 1408 (1993)

    Article  Google Scholar 

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Ambika, G., Menon, K. Fractal patterns on the onset of coherent structures in a coupled map lattice. Pramana - J Phys 59, L155–L161 (2002). https://doi.org/10.1007/s12043-002-0040-5

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  • DOI: https://doi.org/10.1007/s12043-002-0040-5

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