Advertisement

Natural Computing

, Volume 8, Issue 3, pp 473–492 | Cite as

Information processing with structured excitable medium

  • J. Gorecki
  • J. N. Gorecka
  • Y. Igarashi
Article

Abstract

There are many ways in which a nonlinear chemical medium can be used for information processing. Here we are concerned with an excitable medium and the straightforward method of information coding: a single excitation pulse represents a bit of information and a group of excitations forms a message. Our attention is focused on a specific type of nonhomogeneous medium that has an intentionally introduced geometrical structure of regions characterized by different excitability levels. We show that in information processing applications the geometry plays an equally important role as the dynamics of the medium and allows one to construct devices that perform complex signal processing operations even for a relatively simple kinetics of the reactions involved. In the paper we review a number of published chemical realizations of simple information processing devices like logical gates or memory cells and we show that by combining these devices as building blocks the medium can perform complex operations like for example counting of arriving excitations. We also present a new, simple realizations of chemical signal diode that transmits pulses in one direction only.

Keywords

Excitability Information processing Oregonator model Belousov–Zhabotinsky reaction 

References

  1. Adamatzky A, De Lacy Costello B et al (2005) Reaction-diffusion computers. Elsevier Science, AmsterdamGoogle Scholar
  2. Agladze K, Aliev RR et al (1996) Chemical diode. J Phys Chem 100:13895–13897CrossRefGoogle Scholar
  3. Amemiya T, Ohmori T et al (2000) An Oregonator-class model for photoinduced behavior in the Ru(bpy)3 2+-catalyzed Belousov-Zhabotinsky reaction. J Phys Chem A 104:336–344CrossRefGoogle Scholar
  4. Armstrong GR, Taylor AF et al (2004) Modelling wave propagation across a series of gaps. Phys Chem Chem Phys 6:4677–4681CrossRefGoogle Scholar
  5. Calude CS, Paun G (2002) Computing with cells and atoms. Taylor and Francis, LondonGoogle Scholar
  6. Dolnik M, Marek M (1991) Phase excitation curves in the model of forced excitable reaction system. J Phys Chem. 95:7267–7272CrossRefGoogle Scholar
  7. Dolnik M, Finkeova I et al (1989) Dynamics of forced excitable and oscillatory chemical-reaction systems. J Phys Chem 93:2764–2774CrossRefGoogle Scholar
  8. Dolnik M, Marek M et al (2002) Resonances in periodically forced excitable systems. J Phys Chem 96:3218–3224CrossRefGoogle Scholar
  9. Feynman RP, Allen RW, Heywould T (2000) Feynman lectures on computation. Perseus Books, New YorkGoogle Scholar
  10. Field RJ, Noyes RM (1974) Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J Chem Phys 60:1877–1884CrossRefGoogle Scholar
  11. Finkeova I, Dolnik M et al (1990) Excitable chemical reaction systems in a continuous stirred tank reactor. J Phys Chem 94:4110–4115CrossRefGoogle Scholar
  12. Gaspar V, Bazsa G et al (1983) The influence of visible light on the Belousov-Zhabotinskii oscillating reactions applying different catalysts. Z Phys Chem (Leipzig) 264:43–48Google Scholar
  13. Gorecki J, Kawczynski AL (1996) Molecular dynamics simulations of a thermochemical system in bistable and excitable regimes. J Phys Chem 100:19371–19379CrossRefGoogle Scholar
  14. Gorecka J, Gorecki J (2003) T-shaped coincidence detector as a band filter of chemical signal frequency. Phys Rev E 67:067203CrossRefGoogle Scholar
  15. Gorecki J, Gorecka JN (2005) On mathematical description of information processing in chemical systems. In: Aiki T, Niezgodka M et al (eds) Mathematical approach to nonlinear phenomena; Modeling, analysis and simulations, vol 23. GAKUTO International Series, Mathematical Sciences and Applications, pp 73–90Google Scholar
  16. Gorecka J, Gorecki J (2006) Multiargument logical operations performed with excitable chemical medium. J Chem Phys 124:084101CrossRefGoogle Scholar
  17. Gorecki J, Yoshikawa K et al (2003) On chemical reactors that can count. J Phys Chem A 107:1664–1669CrossRefGoogle Scholar
  18. Gorecki J, Gorecka JN et al (2005) 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 72:046201CrossRefGoogle Scholar
  19. Gorecka J, Gorecki J et al (2007) One dimensional chemical signal diode constructed with two non-excitable barriers. J Phys Chem A 111:885–889CrossRefGoogle Scholar
  20. Haken H (2002) Brain dynamics. Springer, BerlinzbMATHGoogle Scholar
  21. Kapral R, Showalter K (1995) Chemical waves and patterns. Kluwer, DordrechtGoogle Scholar
  22. Krischer K, Eiswirth M et al (1992) Oscillatory CO oxidation on Pt(110): modeling of temporal self-organization. J Chem Phys 96:9161–9172CrossRefGoogle Scholar
  23. Krug HJ, Pohlmann L et al (1990) Analysis of the modified complete Oregonator accounting for oxygen sensitivity and photosensitivity of Belousov–Zhabotinskii systems. J Phys Chem 94:4862–4866CrossRefGoogle Scholar
  24. Kuhnert L, Agladze KI et al (1989) Image processing using light-sensitive chemical waves. Nature 337:244–247CrossRefGoogle Scholar
  25. Kuramoto Y (1984) Chemical oscillations, waves, and turbulence. Springer-Verlag, BerlinzbMATHGoogle Scholar
  26. Lazar A, Noszticzius Z et al (1995) Chemical pulses in modified membranes I. Developing the technique. Physica D 84:112–119CrossRefGoogle Scholar
  27. Mikhailov AS, Showalter K (2006) Control of waves, patterns and turbulence in chemical systems. Phys Rep 425:79–194CrossRefMathSciNetGoogle Scholar
  28. Motoike I, Yoshikawa K (1999) Information operations with an excitable field. Phys Rev E 59:5354–5360CrossRefGoogle Scholar
  29. Motoike IN, Yoshikawa K et al (2001) Real-time memory on an excitable field. Phys Rev 63:036220Google Scholar
  30. Murray JD (1989) Mathematical biology. Springer-Verlag, BerlinzbMATHGoogle Scholar
  31. Noszticzuis Z, Horsthemke W et al (1987) Sustained chemical pulses in an annular gel reactor: a chemical pinwheel. Nature 329:619–620CrossRefGoogle Scholar
  32. Rambidi NG, Maximychev AV (1997) towards a biomolecular computer. information processing capabilities of biomolecular nonlinear dynamic media. BioSystems 41:195–211CrossRefGoogle Scholar
  33. Sielewiesiuk J, Gorecki J (2001a) Chemical impulses in the perpendicular junction of two channels. Acta Phys Pol B 32:1589–1603Google Scholar
  34. Sielewiesiuk J, Gorecki J (2001b) Logical functions of a cross junction of excitable chemical media. J Phys Chem A 105:8189–8195CrossRefGoogle Scholar
  35. Sielewiesiuk J, Gorecki J (2002a) On complex transformations of chemical signals passing through a passive barrier. Phys Rev E 66, 016212CrossRefGoogle Scholar
  36. Sielewiesiuk J, Gorecki J (2002b) Passive barrier as a transformer of chemical signal frequency. J Phys Chem A 106:4068–4076CrossRefGoogle Scholar
  37. Steinbock O, Toth A et al (1995) Navigating complex labyrinths—optimal paths from chemical waves. Science 267:868–871CrossRefGoogle Scholar
  38. Suzuki K, Yoshinobu T et al (2000) Unidirectional propagation of chemical waves through microgaps between zones with different excitability. J Phys Chem A 104:6602–6608CrossRefGoogle Scholar
  39. Tanaka M, Nagahara H et al (2007) Survival versus collapse: abrupt drop of excitability kills the traveling pulse, while gradual change results in adaptation. Phys Rev E 76:016205CrossRefGoogle Scholar
  40. Taylor AF, Armstrong GR et al (2003) Propagation of chemical waves across inexcitable gaps. Phys Chem Chem Phys 5:3928–3932CrossRefGoogle Scholar
  41. Tero A, Kobayashi R et al (2006) Physarum solver: a biologically inspired method of road-network navigation. Physica A 363:115–119CrossRefGoogle Scholar
  42. Toth A, Horvath D et al (2001) Unidirectional wave propagation in one spatial dimension. Chem Phys Lett 345:471–474CrossRefGoogle Scholar
  43. Volford A, Simon PL et al (1999) Rotating chemical waves: theory and experiments. Physica A 274:30–49CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  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

Personalised recommendations