Analysis of the influence of random noises for self-oscillating chemical reactions by a Monte-Carlo method on supercomputers

S. S. Artemiev^ab, A. A. Ivanov<sup>a

a</sup> Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Acad. Lavrentyev av., 630090 Novosibirsk
^b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk

Abstract: We study the question of the influence of external and internal random noises on the behavior of the concentrations of the components of chemical reactions and the use of statistical modeling for the solutions of the appearing stochastic differential equations. The results of numerical experiments are given. For the analysis of numerical solutions, we use frequency characteristics generalizing an integral curve and the phase portrait. The numerical experiments showed that even a random noise with low intensity causes all kinds of transitions from one oscillation mode to another in the solutions to the SDEs.

Keywords: stochastic differential equation, cumulative frequency curve, frequency phase portrait, generalized Euler method, concentration, chemical reaction.

UDC: 519.676

Received: 14.12.2015

DOI: 10.17377/sibjim.2016.19.402

 English version: Journal of Applied and Industrial Mathematics, 2016, 10:4, 468–473

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