WHITE NOISE EFFECT IN THE DYNAMIC MODEL OF THE ELECTROCHEMICAL REACTION


Cite item

Abstract

The work is devoted to the problem of the Gaussian white noise influence on a canard cycle in a dynamic model of an electrochemical reaction. This study is conducted on the example of an electrochemical reaction of the Cooper-Slyter type. An analysis of noise-induced transitions was performed, the effect of external disturbances on the limit cycle is investigated, the sensitivity of the cycle to the noise is found. A critical noise intensity, at which the small-amplitude oscillations are transformed into mixedmode oscillations, is obtained. It is shown that an increase in the intensity of random perturbations can lead to significant deformations of the modes in the model up to their destruction.

About the authors

N. M. Firstova

Samara National Research University

Author for correspondence.
Email: morenov@ssau.ru

References

  1. Berglund N., Gentz B., Kuehn C. Hunting french ducks in a noisy environment. Journal of Differential Equations, 2012, Vol. 252, no. 9, pp. 4786–4841. doi: 10.1016/j.jde.2012.01.015 .
  2. Grasman J. Asymptotic analysis of nonlinear systems with small stochastic perturbations. Mathematics and Computers in Simulation, 1989, Vol. 31. no. 1-2, pp. 41–54. Available at: https://socionet.ru/d/repec:eee:matcom:v:31:y:1989:i:1:p:41-54/http://www.sciencedirect.com/science/article/pii/0378475489900529 .
  3. Berthier F., Diard J.P., Nugues S. On the nature of the spontaneous oscillations observed for the Koper-Sluyters electrocatalitic reaction. Journal of Electroanalytical Chemistry, 1997, Vol. 436, no. 1, pp. 35–42 .
  4. Koper M.T.M., Sluyters J.H. Instabilities and oscillations in simple models of electrocatalytic surface reactions. Journal of Electroanalytical Chemistry, 1994, Vol. 371, no. 1, p. 149. DOI: https://doi.org/10.1016/0022-0728(93)03248-N .
  5. Firstova N. Issledovanie kriticheskikh yavlenii v modeli elektrokhimicheskogo reaktora . Vestnik of Samara State University, 2013, Vol. 110, no. 9/2, pp. 221–226. Available at: http://repo.ssau.ru/bitstream/Informacionnye-tehnologii-i-nanotehnologii/Modelirovanie-kriticheskih-yavlenii-vmodeli-elektrohimicheskogo-reaktora-s-uchetom-vneshnego-soprotivleniya-cepi-63841/1/paper%20180_1020-1024.pdf .
  6. Shchepakina E.A., Firstova N.M. Study of oscillatory processes in the one model of electrochemical reactor. CEUR Workshop Proceedings, 2016, Vol. 1638, pp. 731–741. doi: 10.18287/1613-0073-2016-1638-731-741 .
  7. Firstova N., Shchepakina E. Conditions for the critical phenomena in a dynamic model of an electrocatalytic reaction. Journal of Physics: Conference Series, 2017, Vol. 811, pp. 151 .
  8. Firstova N., Shchepakina E. Modelling of Critical Conditions for an Electrochemical Reactor Model. Procedia Engineering, 2017, Vol. 201, pp. 495–502. doi: 10.1016/j.proeng.2017.09.621 .
  9. Shchepakina E.A. Usloviya bezopasnosti vosplameneniya goryuchei zhidkosti v poristom izolyatsionnom materiale . Sibirskii zhurnal industrialnoi matematiki , 2002, Vol. 5, no. 3(11), pp. 162–169. Available at: http://mi.mathnet.ru/sjim253 .
  10. Shchepakina E.A. Singulyarnye vozmushcheniya v zadache modelirovaniya bezopasnykh rezhimov goreniya . Matem. modelirovanie , 2003, Vol. 15, no. 8. pp. 113–117. Available at: http://mi.mathnet.ru/mm414 .
  11. Shchepakina E.A. Black swans and canards in self-ignition problem. Nonlinear Anal.: Real World Appl., 2003, Vol. 4, pp. 45–50. DOI: https://doi.org/10.1016/S1468-1218(02)00012-3 .
  12. Shchepakina E.A. Singulyarno vozmushchennye modeli goreniya v mnogofaznykh sredakh . Sibirskii zhurnal industrialnoi matematiki , 2003, Vol. 6, no. 4(16), pp. 142–157. Available at: http://mi.mathnet.ru/sjim429 .
  13. Golodova E.S., Shchepakina E.A. Modelirovanie bezopasnykh protsessov goreniya s maksimalnoi temperaturoi . Matem. modelirovanie , 2008, Vol. 20, no. 5. pp. 55–68. Available at: http://mi.mathnet.ru/mm2390 .
  14. Sobolev V.A., Shchepakina E.A. Reduktsiya modelei i kriticheskie yavleniya v makrokinetike . M.: Fizmatlit, 2010, 319 p. .
  15. Shchepakina E.A. Critical phenomena in a model of fuel’s heating in a porous medium. CEUR Workshop Proceedings, 2015, Vol. 1490, pp. 179–189. doi: 10.18287/1613-0073-2015-1490-179-189 .
  16. De Swart H.E., Grasman J. Effect of stochastic perturbations on a low-order spectral model of the atmospheric circulation Tellus, 1987, Vol. 39A, pp. 10–24. DOI: https://doi.org/10.3402/tellusa.v39i1.11735.
  17. Grasman J. Asymptotic analysis of nonlinear systems with small stochastic perturbations. Mathematics and Computers in Simulation, 1989, Vol. 31, pp. 41–54. Available at: http://www.sciencedirect.com/science/article/pii/0378475489900529 .
  18. Bashkirtseva I.A., Ryashko L.B. Sensitivity analysis of the stochastically and periodically forced Brusselator. Physica A, 2000, Vol. 278, pp. 126–139. DOI: https://doi.org/10.1016/S0378-4371(99)00453 .
  19. Bashkirtseva I.A., Ryashko L.B. Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system Frontiers in Life Science, 2011, Vol. 5, pp. 141–148. DOI: https://doi.org/10.1080/21553769.2012.702666.

Copyright (c) 2019 Н. М. Фирстова

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies