Information Processing with Structured Chemical Excitable Medium

  • J. Gorecki
  • J. N. Gorecka
  • Y. Igarashi
  • K. Yoshikawa
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 1)

Abstract

It is well known that an excitable medium can be used for information processing with pulses of excitation. In such medium messages can be coded or in the number of pulses or in the sequences of times separating subsequent excitations. Information is processed as the result of two major effects: interactions between pulses and interactions between a pulse and the environment. The properties of excitable medium provide us with a number of features remaining those characterizing biological information processing. For example, pulses of excitation appear as the result of an external stimulus and they can propagate in a homogeneous medium with a constant velocity and a stationary shape dissipating medium energy.

In the paper we focus our attention on a quite specific type of nonhomogeneous medium that has intentionally introduced geometrical structure of regions characterized by different excitability levels. Considering numerical simulations based on simple reaction-diffusion models and experiments with Bielousov-Zhabotinsky reaction we show that in information processing applications the geometry plays equally important role as the dynamics of the medium. A chemical realization of simple information processing devices like logical gates or memory cells are presented. Combining these devices as building blocks we can perform complex signal processing operations like, for example, excitation counting. We also demonstrate that a structured excitable medium can perform sensing functions because it is able to determine a distance separating observer from the source or sense the rate of changes in excitability level. Talking about the perspectives we present ideas for programming information processing medium with excitation pulses.

Keywords

Information processing excitability BZ-reaction Oregonator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Feynman, R.P., Allen, R.W., Heywould, T.: Feynman Lectures on Computation. Perseus Books, New York (2000)Google Scholar
  2. 2.
    Calude, C.S., Paun, G.: Computing with cells and atoms. Taylor and Francis, London (2002)Google Scholar
  3. 3.
    Adleman, L.M.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  4. 4.
    Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction-Diffusion Computers. Elsevier Science, UK (2005)Google Scholar
  5. 5.
    Kapral, R., Showalter, K.: Chemical Waves and Patterns. Kluwer Academic, Dordrecht (1995)Google Scholar
  6. 6.
    Kuhnert, L., Agladze, K.I., Krinsky, V.I.: Image processing using light-sensitive chemical waves. Nature 337, 244–247 (1989)CrossRefGoogle Scholar
  7. 7.
    Rambidi, N.G., Maximychev, A.V.: Towards a Biomolecular Computer. Information Processing Capabilities of Biomolecular Nonlinear Dynamic Media. BioSystems 41, 195–211 (1997)CrossRefGoogle Scholar
  8. 8.
    Szymanski, J.: Private information (2008)Google Scholar
  9. 9.
    Kawczynski, A.L., Legawiec, B.: Two-dimensional model of a reaction-diffusion system as a typewriter. Phys. Rev. E 64, 056202(1-4) (2001)Google Scholar
  10. 10.
    Kawczynski, A.L., Legawiec, B.: A two-dimensional model of reaction-diffusion system as a generator of Old Hebrew letters. Pol. J. Chem. 78, 733–739 (2004)Google Scholar
  11. 11.
    Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Springer, Berlin (1984)MATHGoogle Scholar
  12. 12.
    Mikhailov, A.S., Showalter, K.: Control of waves, patterns and turbulence in chemical systems. Phys. Rep. 425, 79–194 (2006)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Krischer, K., Eiswirth, M., Ertl, G.J.: Oscillatory CO oxidation on Pt(110): modelling of temporal self-organization. J.Chem. Phys. 96, 9161–9172 (1992)CrossRefGoogle Scholar
  14. 14.
    Gorecki, J., Kawczynski, A.L.: Molecular dynamics simulations of a thermochemical system in bistable and excitable regimes. J. Phys. Chem. 100, 19371–19379 (1996)CrossRefGoogle Scholar
  15. 15.
    Steinbock, O., Toth, A., Showalter, K.: Navigating complex labyrinths - optimal paths from chemical waves. Science 267, 868–871 (1995)CrossRefGoogle Scholar
  16. 16.
    Toth, A., Showalter, K.: Logic gates in excitable media. J. Chem. Phys. 103, 2058–2066 (1995)CrossRefGoogle Scholar
  17. 17.
    Field, R.J., Noyes, R.M.: Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877–1884 (1974)CrossRefGoogle Scholar
  18. 18.
    Gaspar, V., Bazsa, G., Beck, M.T.: The influence of visible light on the Belousov–Zhabotinskii oscillating reactions applying different catalysts. Z. Phys. Chem(Leipzig) 264, 43–48 (1983)Google Scholar
  19. 19.
    Krug, H.J., Pohlmann, L., Kuhnert, L.: Analysis of the modified complete Oregonator accounting for oxygen sensitivity and photosensitivity of Belousov–Zhabotinskii systems. J. Phys. Chem. 94, 4862–4866 (1990)CrossRefGoogle Scholar
  20. 20.
    Amemiya, T., Ohmori, T., Yamaguchi, T.: An Oregonator-class model for photoinduced Behavior in the Ru(bpy)\(_{3}^{2+}\)–Catalyzed Belousov–Zhabotinsky reaction. J. Phys. Chem. A. 104, 336–344 (2000)CrossRefGoogle Scholar
  21. 21.
    Motoike, I., Yoshikawa, K.: Information Operations with an Excitable Field. Phys. Rev. E 59, 5354–5360 (1999)CrossRefGoogle Scholar
  22. 22.
    Gorecki, J., Yoshikawa, K., Igarashi, Y.: On chemical reactors that can count. J. Phys. Chem. A 107, 1664–1669 (2003)CrossRefGoogle Scholar
  23. 23.
    Gorecka, J., Gorecki, J.: Multiargument logical operations performed with excitable chemical medium. J. Chem. Phys. 124, 084101 (2006)CrossRefGoogle Scholar
  24. 24.
    Haken, H.: Brain Dynamics. Springer Series in Synergetics. Springer, Berlin (2002)MATHGoogle Scholar
  25. 25.
    Agladze, K., Aliev, R.R., Yamaguchi, T., Yoshikawa, K.: Chemical diode. J. Phys. Chem. 100, 13895–13897 (1996)CrossRefGoogle Scholar
  26. 26.
    Sielewiesiuk, J., Gorecki, J.: Chemical impulses in the perpendicular junction of two channels. Acta Phys. Pol. B 32, 1589–1603 (2001)Google Scholar
  27. 27.
    Sielewiesiuk, J., Gorecki, J.: Logical functions of a cross junction of excitable chemical media. J. Phys. Chem. A 105, 8189–8195 (2001)CrossRefGoogle Scholar
  28. 28.
    Dolnik, M., Finkeova, I., Schreiber, I., Marek, M.: Dynamics of forced excitable and oscillatory chemical-reaction systems. J. Phys. Chem. 93, 2764–2774 (1989); Finkeova, I., Dolnik, M., Hrudka, B., Marek, M.: Excitable chemical reaction systems in a continuous stirred tank reactor. J. Phys. Chem. 94, 4110–4115 (1990); Dolnik, M., Marek, M.: Phase excitation curves in the model of forced excitable reaction system. J. Phys. Chem. 95, 7267–7272 (1991); Dolnik, M., Marek, M., Epstein, I.R.: Resonances in periodically forced excitable systems. J. Phys. Chem. 96, 3218–3224 (1992) Google Scholar
  29. 29.
    Suzuki, K., Yoshinobu, T., Iwasaki, H.: Unidirectional propagation of chemical waves through microgaps between zones with different excitability. J. Phys. Chem. A 104, 6602–6608 (2000)CrossRefGoogle Scholar
  30. 30.
    Sielewiesiuk, J., Gorecki, J.: On complex transformations of chemical signals passing through a passive barrier. Phys. Rev. E 66, 016212 (2002); Sielewiesiuk, J., Gorecki, J.: Passive barrier as a transformer of chemical signal frequency. J. Phys. Chem. A 106, 4068–4076 (2002)CrossRefGoogle Scholar
  31. 31.
    Taylor, A.F., Armstrong, G.R., Goodchild, N., Scott, S.K.: Propagation of chemical waves across inexcitable gaps. Phys. Chem. Chem. Phys. 5, 3928–3932 (2003)CrossRefGoogle Scholar
  32. 32.
    Armstrong, G.R., Taylor, A.F., Scott, S.K., Gaspar, V.: Modelling wave propagation across a series of gaps. Phys. Chem. Chem. Phys. 6, 4677–4681 (2004)CrossRefGoogle Scholar
  33. 33.
    Gorecki, J., Gorecka, J.N., Yoshikawa, K., Igarashi, Y., Nagahara, H.: Sensing the distance to a source of periodic oscillations in a nonlinear chemical medium with the output information coded in frequency of excitation pulses. Phys. Rev. E 72, 046201 (2005)CrossRefGoogle Scholar
  34. 34.
    Tanaka, M., Nagahara, H., Kitahata, H., Krinsky, V., Agladze, K., Yoshikawa, K.: Survival versus collapse: Abrupt drop of excitability kills the traveling pulse, while gradual change results in adaptation. Phys. Rev. E 76, 016205 (2007)CrossRefGoogle Scholar
  35. 35.
    Lázár, A., Noszticzius, Z., Försterling, H.-D., Nagy-Ungvárai, Z.: Chemical pulses in modified membranes I. Developing the technique. Physica D 84, 112–119 (1995); Volford, A., Simon, P.L., Farkas, H., Noszticzius, Z.: Rotating chemical waves: theory and experiments. Physica A 274, 30–49 (1999)CrossRefGoogle Scholar
  36. 36.
    Nagai, Y., Gonzalez, H., Shrier, A., Glass, L.: Paroxysmal Starting and Stopping of Circulatong Pulses in Excitable Media. Phys. Rev. Lett. 84, 4248–4251 (2000)CrossRefGoogle Scholar
  37. 37.
    Noszticzuis, Z., Horsthemke, W., McCormick, W.D., Swinney, H.L., Tam, W.Y.: Sustained chemical pulses in an annular gel reactor: a chemical pinwheel. Nature 329, 619–620 (1987)CrossRefGoogle Scholar
  38. 38.
    Motoike, I.N., Yoshikawa, K., Iguchi, Y., Nakata, S.: Real–Time Memory on an Excitable Field. Phys. Rev. E 63, 036220 (2001)CrossRefGoogle Scholar
  39. 39.
    Gorecki, J., Gorecka, J.N.: On mathematical description of information processing in chemical systems. In: Mathematical Approach to Nonlinear Phenomena; Modeling, Analysis and Simulations, GAKUTO International Series, Mathematical Sciences and Applications, vol. 23, pp. 73–90 (2005) ISBN 4762504327Google Scholar

Copyright information

© Springer Tokyo 2009

Authors and Affiliations

  • J. Gorecki
    • 1
    • 2
  • J. N. Gorecka
    • 3
  • Y. Igarashi
    • 1
  • K. Yoshikawa
    • 4
  1. 1.Institute of Physical ChemistryPolish Academy of ScienceWarsawPoland
  2. 2.Faculty of Mathematics and Natural SciencesCardinal Stefan Wyszynski UniversityWarsawPoland
  3. 3.Institute of PhysicsPolish Academy of SciencesWarsawPoland
  4. 4.Department of Physics, Graduate School of ScienceKyoto UniversityKyotoJapan

Personalised recommendations