Computational Method for Searching Singular Points on the Plane of Complex Time for Research of Determinated-Chaotic Systems (Using the Example of E. Lorenz System)

Authors

  • Bunyakin A.V. Kuban State University, Krasnodar, Российская Федерация
  • Pshikova I.S. Kuban State University, Krasnodar, Российская Федерация

UDC

531

DOI:

https://doi.org/10.31429/vestnik-17-1-2-69-80

Abstract

The general scheme of search and recognition (identification) of singular points of the solution of dynamic systems is present. Under singular points we understand not a features of the phase flow, but the poles of the functions of the solution components for analytical continuation into the plane of complex time. Pole orders may be different for different components. As examples for calculation, precisely known system exhibiting deterministic chaotic behavior – E. Lorentz system, and also indicates a general scheme for matching of the differential dynamic system solution with the special integer sequence (quantization).
The introduction describes a method for searching for singular points on the plane of complex time, which is a specific variant of numerical integration with the optimal choice of the direction of the next step. Optimization is the minimization of the number of steps, that is, ultimately – the computational time. The second part of the paper describes an algorithm for searching for singular points of the layer closest to the real time axis, and this algorithm is numerically implemented for the Lorentz system. The third (final) part of the paper describes a possible application of the method for constructing quantum-mechanical models of multielectronic systems.

Keywords:

dynamical systems, deterministic chaos, analytic continuation

Author Infos

Aleksey V. Bunyakin

канд. физ.–мат. наук, доцент кафедр математических и компьютерных методов Кубанского государственного университета, оборудования нефтяных и газовых промыслов Кубанского государственного технологического университета, кафедры нефтегазового дела и землеустройства Майкопского государственного технологического университета

e-mail: alex.bunyakin@mail.ru

Irina S. Pshikova

студентка факультета математики и компьютерных наук Кубанского государственного университета, старший лаборант кафедры математических и компьютерных методов Кубанского государственного университета

e-mail: ira.pshikova.98@gmail.com

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Issue

2020. Vol. 17. No. 1. Part 2

Section

Physics

Pages

69-80

Submitted

2020-01-24

Published

2020-03-31

How to Cite

Bunyakin A.V., Pshikova I.S. Computational Method for Searching Singular Points on the Plane of Complex Time for Research of Determinated-Chaotic Systems (Using the Example of E. Lorenz System). Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 1, pp. 69-80. DOI: https://doi.org/10.31429/vestnik-17-1-2-69-80 (In Russian)

Copyright (c) 2020 Bunyakin A.V., Pshikova I.S.

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