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Part of the book series: Nonlinear Phenomena and Complex Systems ((NOPH,volume 8))

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Abstract

We show that the presence of undulated boundaries can induce the formation of spatially chaotic, stationary, and stable structures in models as simple as the Fisher-Kolmogorov equation, which does not display any kind of chaos under common boundaries.

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References

  1. H. Bai-Lin, Chaos (World Scientific, Singapore 1990).

    MATH  Google Scholar 

  2. M.C. Cross, P.C. Hohenberg, Science 263, 1569 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. P. Coullet, C. Elphick, and D. Repaux, Phys. Rev. Lett. 58, 431 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  4. E. Hernández-García, M. San Miguel, R. Toral, and J. Vinals, Physica D 61, 159 (1992).

    Article  ADS  MATH  Google Scholar 

  5. R. Montagne, E. Hernández-García, M. San Miguel, Phys. Rev. Lett. 77, 267 (1996)

    Article  ADS  Google Scholar 

  6. R. Montagne, E. Hernández-García, A. Amengual, M. San Miguel, Phys. Rev. E56, 151 (1997).

    MathSciNet  ADS  Google Scholar 

  7. N.J. Balmforth, Annu. Rev. Fluid Mech. 27, 335 (1996).

    Article  ADS  Google Scholar 

  8. H-C. Chang, Annu. Rev. Fluid Mech. 26, 103 (1994).

    Article  ADS  Google Scholar 

  9. Y.A. Demekhin, G.Yu. Tokarev, V.Ja. Shkadov, Physica D52, 338 (1991)

    MathSciNet  MATH  Google Scholar 

  10. M.I. Rabinovich, A.L. Fabrikant, and L. Sh. Tsimring, Sov. Phys. Usp. 35, 629 (1992).

    Article  ADS  Google Scholar 

  11. Malkov, Physica D 95, 62 (1996).

    Article  MATH  Google Scholar 

  12. S.W. Jones, 0.M. Thomas, H. Aref, J. Fluid Mech. 209, 335 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  13. Y. LeGuer et al., Experimental study of chaotic advection in a twisted duct flow, preprint.

    Google Scholar 

  14. J.H.E. Cartwright, M. Feingold, and O. Piro, in Proceedings of the NATO ARW “Mixing, Chaos, and Turbulence”, H. Chaté and E. Villermaux, editors, (1997).

    Google Scholar 

  15. J. D. Gunton, M. San Miguel and P.S. Sahni, The dynamics of first order phase transitions in Phase Transitions and Critical Phenomena, vol. 8. C. Domb and J. L. Lebowitz, Eds. (Academic Press, New York, 1983).

    Google Scholar 

  16. R. Montagne, E. Hernández-García, M. San Miguel, Physica D 96, 47 (1996)

    MathSciNet  MATH  Google Scholar 

  17. M. San Miguel, R. Montagne, A. Amengual, E. Hernández-García, in Instabilities and Nonequilibrium Structures, V. E. Tirapegui and W. Zeller, Eds. (Kluwer Academic Publishers, Dordrecht, 1996).

    Google Scholar 

  18. P. Collet, Nonlinearity 7, 1175 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. V.M. Eguíluz, E. Hernández-García, O. Piro, S. Balle, Phys. Rev. E 60, 6571 (1999).

    Article  ADS  Google Scholar 

  20. V.M. Eguíluz, P. Alstrøm, E. Hernández-García, O. Piro, Phys. Rev. E 59 2822 (1999)

    Article  ADS  Google Scholar 

  21. V.M. Eguíluz, E. Hernández-García, O. Piro, Int. J. Bif. Chaos 9, 2209 (1999)

    Article  MATH  Google Scholar 

  22. V.M. Eguíluz, E. Hernández-García, O. Piro, Physica A 283, 48 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  23. V.M. Eguíluz, E. Hernández-García, O. Piro, Phys. Rev. E 64, 036205 (2001)

    Article  ADS  Google Scholar 

  24. I. Sendiña-Nadal, V. Pérez-Muñuzuri, V.M. Egufluz, E. Hernández-García, O. Piro, Phys. Rev. E 64, 046208 (2001).

    ADS  Google Scholar 

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© 2004 Kluwer Academic Publishers

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Eguíluz, V.M., Hernández-García, E., Piro, O. (2004). Boundary-Forced Spatial Chaos. In: Descalzi, O., Martínez, J., Tirapegui, E. (eds) Instabilities and Nonequilibrium Structures VII & VIII. Nonlinear Phenomena and Complex Systems, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2149-7_13

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  • DOI: https://doi.org/10.1007/978-1-4020-2149-7_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-015-6994-1

  • Online ISBN: 978-1-4020-2149-7

  • eBook Packages: Springer Book Archive

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