Geodesic
Analysis of the stochastic excitement in a model of flow reactor
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 3, pp. 269-278.

Voir la notice de l'article provenant de la source Math-Net.Ru

A probabilistic mechanism of the stochastic excitement in a model of flow reactor is studied. To analyze this phenomenon in regions of mono- and bistability the stochastic sensitivity function technique and the method of confidence ellipses are used.
Keywords: random disturbances, excitability, stochastic sensitivity, confidence ellipses. 
@article{JSFU_2016_9_3_a0,
     author = {Irina A. Bashkirtseva and Polina M. Fominykh},
     title = {Analysis of the stochastic excitement in a model of flow reactor},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {269--278},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_3_a0/}
}
TY  - JOUR
AU  - Irina A. Bashkirtseva
AU  - Polina M. Fominykh
TI  - Analysis of the stochastic excitement in a model of flow reactor
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2016
SP  - 269
EP  - 278
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2016_9_3_a0/
LA  - en
ID  - JSFU_2016_9_3_a0
ER  - 
%0 Journal Article
%A Irina A. Bashkirtseva
%A Polina M. Fominykh
%T Analysis of the stochastic excitement in a model of flow reactor
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2016
%P 269-278
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2016_9_3_a0/
%G en
%F JSFU_2016_9_3_a0
Irina A. Bashkirtseva; Polina M. Fominykh. Analysis of the stochastic excitement in a model of flow reactor. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 3, pp. 269-278. http://geodesic.mathdoc.fr/item/JSFU_2016_9_3_a0/

[1] W. Horsthemke, R. Lefever, Noise-Induced Transitions, Springer, Berlin, 1984 | MR | Zbl

[2] Yu. I. Neimark, P. S. Landa, Stochastic and chaotic oscillations, Nauka, M., 1987 (in Russian) | MR

[3] M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, D. Abbott, Stochastic resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization, Cambridge University Press, 2008 | Zbl

[4] V. S. Anishchenko, V. V. Astakhov, A. B. Neiman, T. E. Vadivasova, L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development, Springer-Verlag, Berlin–Heidelberg, 2007 | MR

[5] K. Matsumoto, I. Tsuda, “Noise-induced order”, J. Stat. Phys., 33 (1983), 87–106 | DOI | MR

[6] J. B. Gao, S. K. Hwang, J. M. Liu, When can noise induce chaos?, Phys. Rev. Lett., 82 (1999), 113–1135 | DOI

[7] B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Schimansky-Geier, “Effects of noise in excitable systems”, Physics Reports, 392 (2004), 321–424 | DOI

[8] P. S. Landa, Nonlinear Oscillations and Waves in Dynamical Systems, Springer, 1996 | MR

[9] O.V. Ushakov et al., “Coherence resonance near a Hopf bifurcation”, Phys. Rev. Lett., 95 (2005), 123903 | DOI

[10] I. Bashkirtseva, L. Ryashko, H. Schurz, “Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances”, Chaos, Solitons and Fractals, 39 (2009), 72–82 | DOI | MR | Zbl

[11] A. Zakharova, T. Vadivasova et al., “Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator”, Phys. Rev. E, 81 (2010), 011106 | DOI

[12] I. Bashkirtseva, T. Ryazanova, L. Ryashko, “Stochastic bifurcations caused by multiplicative noise in systems with hard excitement of auto-oscillations”, Phys. Rev. E, 92 (2015), 042908 | DOI | MR

[13] V. I. Bykov, S. B. Tsybenova, Nonlinear models of chemical kinetics, Krasand, M., 2011 (in Russian)

[14] A. M. Zhabotinsky, Concentration Auto-Oscillations, Nauka, M., 1974 (in Russian)

[15] B. V. Volter, I. E. Salnikov, Stability of operation modes of chemical reactors, Khimiya, M., 1981 (in Russian)

[16] M. I. Freidlin, A. D. Wentzell, Random Perturbations of Dynamical Systems, Springer, New York, 1984 | MR | Zbl

[17] I. Bashkirtseva, L. Ryashko, “Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect”, Chaos, 21 (2011), 047514 | DOI | Zbl

[18] I. Bashkirtseva, A. B. Neiman, L. Ryashko, “Stochastic sensitivity analysis of the noise-induced excitability in a model of a hair bundle”, Phys. Rev. E, 87 (2013), 052711 | DOI

[19] I. Bashkirtseva, G. Chen, L. Ryashko, “Stochastic equilibria control and chaos suppression for 3D systems via stochastic sensitivity synthesis”, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 3381–3389 | DOI | MR | Zbl