SciELO - Scientific Electronic Library Online

 
vol.51 issue5Modulation of spatial coherence of optical field by means of liquid crystal light modulatorAnharmonic coefficients in high symmetry directions for the diamond structure author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Revista mexicana de física

Print version ISSN 0035-001X

Rev. mex. fis. vol.51 n.5 México Oct. 2005

 

Carta

 

Local induction of spatio-temporal chaos

 

G. Baier, A. Ramírez, I. Amaro, and M. Müller

 

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62210 Cuernavaca, Morelos, México e-mail: baier@servm.fc.uaem.mx

 

Recibido el 3 de diciembre de 2004.
Aceptado el 14 de junio de 2005.

 

Abstract

A periodic perturbation of one excitable system causes a symmetry-breaking instability in two reversibly coupled neighbors. The result is applied to a two-dimensional extended system. Tuning of the local perturbation frequency causes a regular target pattern to switch first to circular chaotic waves and then to chaotic wave fragments. Thus a global order-disorder transition can be induced by local control in an otherwise homogeneous medium.

Keywords: Spatio-temporal chaos; order-disorder transition; local control.

 

Resumen

Una perturbación periódica de un sistema excitable causa un rompimiento de simetría en dos osciladores acoplados reversiblemente. El resultado es aplicado a un sistema extendido en dos dimensiones espaciales. Ajustando la frecuencia de la perturbación local, se cambia un patrón regular de ondas circulares primero a ondas circulares caóticas y después a fragmentos de ondas caóticos. En consecuencia, una transición global orden-desorden se puede inducir bajo control local en un medio homogéneo.

Descriptores: Caos espacio-temporal; transición orden-desorden; control local.

 

PACS: 05.45.Ac; 05.45.Jn; 05.45.Xt

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgements

This work was supported by CONACyT, Mexico (project no. 40885-F). G.B. thanks Sven Sahle for the discussion.

 

References

1. R.A. Grey, A.M. Pertsov, and J. Jalife, Nature 392 (1998) 75;         [ Links ] F.X. Witkowski et al., Nature 392 (1998) 78.         [ Links ]

2. D.F. Smith et al. (eds.), An Atlas of Epilepsy (Parthenon Publishing, New York, 1998);         [ Links ] J. Milton and P. Jung (eds.), Epilepsy as a Dynamic Disease (Springer, New York, 2003).         [ Links ]

3. O.E. Rössler and Z. Naturforsch, 31a (1976) 1168; Y. Kuramoto, Progr. Theor. Phys. Suppl. 64 (1979) 346.         [ Links ]

4. M. Bär and M. Eiswirth, Phys. Rev. E 48 (1993) R1635.         [ Links ]

5. A. Panfilov and P. Hogeweg, Phys. Lett. A 176 (1993) 295;         [ Links ] F.H. Fenton et al., Chaos 12 (2002) 852.         [ Links ]

6. M.C. Mackey and U. an der Heiden, J. Math. Biol. 19 (1984) 211.         [ Links ]

7. O. Steinbock, V.S. Zykov, and S.C. Müller, Nature 366 (1995) 322;         [ Links ] V. Petrov, Q. Ouyang, and H.L. Swinney, Nature 388 (1997) 655;         [ Links ] A.L. Lin et al., Phys. Rev. E62 (2000) 3790.         [ Links ]

8. V.K. Vanag et al., Nature 406 (2000) 389;         [ Links ] M. Hildebrand, H. Skødt, and K. Showalter, Phys. Rev. Lett. 87 (2001) 088303;         [ Links ] I.Z. Kiss, Y. Zhai, and J.L. Hudson, Phys. Rev. Lett. 88 (2002) 238301.         [ Links ]

9. A.T. Winfree, Science 266 (1994) 1003.         [ Links ]

10. G. Baier, S. Sahle, J.-P. Chen, and A. Hoff, J. Chem. Phys. 110 (1999) 3251.         [ Links ]

11. W. Gerstner and W. Kister, Spiking Neuron Models (Cambridge University Press, 2002).         [ Links ]

12. See the chapters by K. Tomita et al., in: A.V. Holden (ed.), Chaos (Princeton University Press, Princeton, 1986).         [ Links ]

13. J. Kaplan and J.A. Yorke, Lecture Notes in Mathematics 730 (1979) 204.         [ Links ]

14. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76 (1996) 1804;         [ Links ] E. Mosekilde, Y. Maistrenko, and D. Postnov, Chaotic Synchronization (World Scientific, Singapore 2002).         [ Links ]

15. J.C. Sommerer and E. Ott, Nature 365 (1993) 138;         [ Links ] E. Ott and J.C. Sommerer, Phys. Lett. A 188 (1994) 39.         [ Links ]

16. N. Platt, E.A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70 (1993) 279.         [ Links ]

17. E. Rodriguez et al., Nature 397 (1999) 430.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License