Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Analytical-Numerical Methods for Search of Hidden Oscillations in Multidimensional Dynamical Systems

Author(s):

I. M. Burkin

Professor, head of department of mathematical analysis,
Department of Mechanics and Mathematics,
Tula State University,
Tula, Russia

i-burkin@yandex.ru

Nguyen Ngoc Hien

graduate student,
Department of Mechanics and Mathematics,
Tula State University,
Tula, Russia

hiendhdt@gmail.com

Abstract:

In nonlinear dynamical systems attractors can be regarded as self-excited and hidden ones. Self-excited attractors can be localized numerically by a standard computational procedure in which after a transient process a trajectory starting from a point of unstable manifold in a neighborhood of equilibrium reaches a state of oscillation; therefore one can easily identify it. In contrast, for a hidden attractor a basin of attraction does not intersect with small neighborhoods of equilibria. Since classical attractors are self-excited they therefore can be obtained numerically by the standard computational procedure. For localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. In this paper we propose a new efficient analytical–numerical method for the study of hidden oscillations in multidimensional dynamical systems.

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