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Journal Nonlinear World №1 for 2014 г.
Article in number:
Simulation of instability oregonators with diffusion
Keywords: model Field-Noyes-Kёros Belousov-Zhabotinsky reaction oregonator diffusion instability nonlinear parabolic equation
Authors:
L.А. Prokudina - Dr.Sci. (Phys.-Math.), Associate Professor, Professor, Applied Mathematics Department, South Ural State University, Chelyabinsk. E-mail: prokudina-la@mail.ru
Abstract:
Model Field-Noyes-Kёros of the Belousov-Zhabotinsky reaction (oregonator) investigated the instability. Identified areas of destabilizing effect of diffusion for different of the coefficient. It is received a nonlinear parabolic equation for the amplitude envelope of the wave packet. Numerical simulation of the amplitude envelope and amplitudes of harmonics of a wave packet is presented.
Pages: 42-47
References

  1. Turing A.M. The chemical basis for morphogenesis // Phil. Trans. Roy. Soc. London. 1952. V. 237. P. 37-72.
  2. Busse H.G. A spatial periodic homo generous reaction // J. Phys. Chem. 1969. V. 73. P. 750.
  3. Herschkowitz-Kaufman M. Structures dissipatives dans une reaction chimique onhomogene // C.R. Acad. Sci. 1970. C. 270. № 12. P. 1049-1052.
  4. Beck M.T., Varadi Z.B. One, two and three-dimensional spatially periodic chemical reactions // Nature (Phys. Sci.). 1972. V. 235. P. 15-16.
  5. Belousov B.P. Sbornik referatov po radiaczionnoj mediczine za 1958 god. M.: Medgiz. 1959. S. 145-148.
  6. Zhabotinskij A.M. Periodicheskij proczess okisleniya malonovoj kisloty' v rastvore (issledovanie kinetiki reakczii Belousova) // Biofizika. 1964. № 9. S. 306-311.
  7. Zhabotinskij A.M. Periodicheskie reakczii okisleniya v zhidkoj faze // DAN SSSR. 1964. T. 157. S. 392-395.
  8. Zhabotinskij A.M. Konczentraczionny'e avtokolebaniya. M.: Nauka. 1974. 179 s.
  9. Noyes R.M., Field R.J., Kyoros E. Oscillations in chemical systems // J. Amer. Chem. Soc. 1972. V. 94. P. 1394-1395.
  10. Field R.J., Kyoros E., Noyes R.M. Oscillations in chemical systems II. Thorough analysis of temporal oscillations in the bromate-cerium-malonic acid system // J. Amer. Chem. Soc. 1972. V. 94. P. 8649-8664.
  11. Edelson D., Field R.J., Noyes R.M. Mechanistic details of the Belousov-Zhabotinskii reaction // Int. J. Chem. Kin. 1975. V. 7. P. 417-432.
  12. Prokudina L.A., Xolpanov L.P. Nelinejnoe razvitie vozmushhenij avtokataliticheskoj reakczii, oslozhnennoj diffuziej // Teoreticheskie osnovy' ximicheskoj texnologii. 2004. T. 38. № 6. S. 675-682.
  13. Prokudina L.A. Diffuzionnaya neustojchivost' v sisteme bromat-czerij-malonovaya kislota // Izv. Chelyab. nauch. czentra UrO RAN. 1999. № 2. S. 22-27.