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October 6, 2021 12:45, Scientific Seminar on Mathematics, Tambov State Technical University (Tambov, October 6, 2021, 12:45, Boiling point, corps L)  


Application of high-precision numerical methods to study attractors of dynamical systems

A. N. Pchelintsev
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A. N. Pchelintsev



Abstract: The speaker considers at the seminar the high-precision numerical methods developed for the study of unstable solutions of systems of ordinary differential equations of chaotic type, as well as the search for approximations to unstable cycles of the Lorenz system.

Supplementary materials: math_seminar_2021.pdf (879.9 Kb)

References
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  2. D. Dudkowski, S. Jafari, T. Kapitaniak, N. V. Kuznetsov, G. A. Leonov, A. Prasad, “Hidden attractors in dynamical systems”, Physics Reports, 637:3 (2016), 1–50  crossref
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  8. The reliable calculations for the Chen system Source code, https://github.com/alpchelintsev/chen_sources
  9. R. Lozi, A. N. Pchelintsev, “A new reliable numerical method for computing chaotic solutions of dynamical systems: the Chen attractor case”, International Journal of Bifurcation and Chaos, 25:13 (2015), 1550187, 10 pp.  crossref
  10. A. N. Pchelintsev, “Chislennoe i fizicheskoe modelirovanie dinamiki sistemy Lorentsa”, Sibirskii zhurnal vychislitelnoi matematiki, 17:2 (2014), 191–201  mathnet
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  14. A. N. Pchelintsev, “An accurate numerical method and algorithm for constructing solutions of chaotic systems”, Journal of Applied Nonlinear Dynamics, 9:2 (2020), 207–221  crossref
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  16. A. N. Pchelintsev, S. Ahmad, “Solution of the Duffing equation by the power series method”, Transactions of the TSTU, 26:1 (2020), 118–123
  17. A. N. Pchelintsev, “A numerical-analytical method for constructing periodic solutions of the Lorenz system”, Differencialnie Uravnenia i Protsesy Upravlenia, 2020, no. 4, 59–75
  18. The programs for finding of periodic solutions in the Lorenz attractor Source code, https://github.com/alpchelintsev/periodic_sols
  19. A. N. Pchelintsev, “Construction of periodic solutions of one class nonautonomous systems of differential equations”, Journal of Applied Mathematics and Physics, 1:3 (2013), 1–4  crossref
  20. V. A. Pliss, Nelokalnye problemy teorii kolebanii, Nauka, M.–L., 1964, 367 pp.
  21. A. Pchelintsev, Dinamicheskaya sistema Lorentsa i vychislitelnyi eksperiment, 2014 https://habrahabr.ru/post/229959/
  22. A. Pchelintsev, Tri tsikla v attraktore Lorentsa, 2017 https://habrahabr.ru/post/329578/
  23. A. Pchelintsev, Ischem tsikly na attraktore Lorentsa v pakete Maxima, 2018 https://habr.com/ru/post/354968/
  24. D. Viswanath, “The Fractal Property of the Lorenz Attractor”, Physica D: Nonlinear Phenomena, 190:1-2 (2004), 115–128  crossref
 
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