- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Periodic spatiotemporal patterns in a two-dimensional two-variable reaction-diffusion model

Andrzej L. Kawczyński* and Marcin Leda

  • Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

  • *Electronic address: alk@ichf.edu.pl
PDF

Phys. Rev. E 73, 056208 – Published 24 May, 2006

DOI: https://doi.org/10.1103/PhysRevE.73.056208

Abstract

Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.

View figure in article

Article Text

References (23)

  1. A. L. Kawczyński and B. Legawiec, Phys. Rev. E 63, 021405 (2001).
  2. W. N. Reynolds, J. E. Pearson, and S. Ponce-Dawson, Phys. Rev. Lett. 72, 2797 (1994).
  3. Y. Nishiura and D. Ueyama, Physica D 150, 137 (2001).
  4. V. Petrov, S. K. Scott, and K. Showalter, Philos. Trans. R. Soc. London, Ser. A 347, 631 (1994).
  5. A. L. Kawczyński and B. Legawiec, Phys. Rev. E 73, 026112 (2006).
  6. S.-I. Ei, M. Mimura, and M. Nagayama, Physica D 165, 176 (2002).
  7. J. Kosek and M. Marek, Phys. Rev. Lett. 74, 2134 (1995).
  8. L. Yang and R. I. Epstein, J. Phys. Chem. A 106, 11676 (2002).
  9. V. K. Vanag and R. I. Epstein, J. Phys. Chem. A 106, 11394 (2002).
  10. V. K. Vanag and I. R. Epstein, J. Chem. Phys. 121, 890 (2004).
  11. A. M. Zhabotinsky, M. D. Eager, and I. R. Epstein, Phys. Rev. Lett. 71, 1526 (1993).
  12. P. K. Brazhnik and J. J. Tyson, Phys. Rev. E 54, 1958 (1996).
  13. P. D. Ronney, Combust. Flame 82, 1 (1990).
  14. M. Mimura and M. Nagayama, Chaos 7, 817 (1997).
  15. S. K. Scott, J. Wang, and K. Showalter, J. Chem. Soc., Faraday Trans. 93, 1733 (1997).
  16. M. Bar, M. Hildebrand, M. Eiswirth, M. Falcke, H. Engel, and M. Neufeld, Chaos 4, 499 (1994).
  17. R. FitzHugh, Biophys. J. 1, 445 (1961).
  18. J. Nagumo, S. Arimoto, and S. Youshizawa, Proc. IRE 50, 2061 (1962).
  19. S. K. Scott, Oscillations, Waves and Chaos in Chemical Kinetics (Oxford University Press, Oxford, 1994).
  20. A. B. Rovinsky and A. M. Zhabotinsky, J. Phys. Chem. 88, 6081 (1984).
  21. A. L. Kawczyński and B. Legawiec, Phys. Rev. E 64, 056202 (2001).
  22. A. Toth, I. Lagzi, and D. Horvath, J. Phys. Chem. 100, 14837 (1996).
  23. P. W. Davies, P. Blanchedeau, E. Dulos, and P. De Kepper, J. Phys. Chem. 102, 8236 (1998).

Outline

Information

Phys. Rev. E 73, 056208– Published 24 May, 2006
  • Received 18 January 2006

© 2006 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation