Geodesic
Analysis of the effect of random noise on the strange attractors of Monte Carlo on a~supercomputer
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 121-134.

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In this paper, we numerically investigate the influence of random noise on the behavior of the trajectories of strange attractors defined by a system of ordinary differential equations. The resulting stochastic differential equations are solved by the generalized Euler method. The results of numerical experiments conducted on a cluster of NKS-30T Siberian Supercomputer Center at ICMMG using the program package PARMONC. For the analysis of the numerical solutions, the frequency characteristics of generalizing the integral curve and the phase portrait are used. 
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S. S. Artemiev; A. A. Ivanov. Analysis of the effect of random noise on the strange attractors of Monte Carlo on a~supercomputer. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 121-134. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a1/

[1] Artem'ev S. S., Chislennye metody resheniya zadachi Koshi dlya sistem obyknovennykh i stokhasticheskikh differentsial'nykh uravnenij, Izd-vo VTS SO RAN, Novosibirsk, 1993

[2] Lojtsyanskij L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[3] Artem'ev S. S., Ivanov A. A., Smirnov D. D., “Novye chastotnye kharakteristiki chislennogo resheniya stokhasticheskikh differentsial'nykh uravnenij”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 18:1 (2015), 15–26

[4] Artem'ev S. S., Korneev V. D., “Chislennoe reshenie stokhasticheskikh differentsial'nykh uravnenij na superkomp'yuterakh”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 14:1 (2011), 5–17 | Zbl

[5] Artem'ev S. S., Ivanov A. A., Korneev V. D., “Chislennyj analiz stokhasticheskikh ostsillyatorov na superkomp'yuterakh”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 15:1 (2012), 31–43 | Zbl

[6] Artem'ev S. S., Korneev V. D., YAkunin M. A., “Chislennoe reshenie stokhasticheskikh differentsial'nykh uravnenij so sluchajnoj strukturoj na superkomp'yuterakh”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 16:4 (2013), 303–311 | Zbl

[7] Anishchenko V. S., Slozhnye kolebaniya v prostykh sistemakh, Nauka, M., 1990 | MR

[8] Nejmark Yu. I., Landa P. S., Stokhasticheskie i khaoticheskie kolebaniya, Nauka, M., 1987 | MR

[9] Marchenko M. A., Mikhajlov G. A., “Raspredelennye vychisleniya po metodu Monte-Karlo”, Avtomatika i telemekhanika, 2007, no. 5, 157–170 | MR | Zbl