On a method of applied symbolic dynamics for investigation of dynamical systems

Research output

Abstract

We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.
Original languageEnglish
Title of host publicationVP Vibroengineering Procedia
Place of PublicationKaunas, Lithuania
PublisherJVE International Ltd.
Pages128-134
Number of pages7
Volume25
DOIs
Publication statusPublished - 25 Jun 2019

Publication series

NameVP Vibroengineering Procedia
PublisherJVE International Ltd.
Volume25
ISSN (Print)2345-0533
ISSN (Electronic)2538-8479

Fingerprint

Dynamical systems
Entropy
Trajectories
Markov processes
Experiments

Scopus subject areas

  • Computer Science(all)

Cite this

Ampilova, N., & Soloviev, I. (2019). On a method of applied symbolic dynamics for investigation of dynamical systems. In VP Vibroengineering Procedia (Vol. 25, pp. 128-134). [20698] (VP Vibroengineering Procedia; Vol. 25). Kaunas, Lithuania: JVE International Ltd.. https://doi.org/10.21595/vp.2019.20698
Ampilova, Natalia ; Soloviev, Igor . / On a method of applied symbolic dynamics for investigation of dynamical systems. VP Vibroengineering Procedia. Vol. 25 Kaunas, Lithuania : JVE International Ltd., 2019. pp. 128-134 (VP Vibroengineering Procedia).
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abstract = "We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.",
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author = "Natalia Ampilova and Igor Soloviev",
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Ampilova, N & Soloviev, I 2019, On a method of applied symbolic dynamics for investigation of dynamical systems. in VP Vibroengineering Procedia. vol. 25, 20698, VP Vibroengineering Procedia, vol. 25, JVE International Ltd., Kaunas, Lithuania, pp. 128-134. https://doi.org/10.21595/vp.2019.20698

On a method of applied symbolic dynamics for investigation of dynamical systems. / Ampilova, Natalia ; Soloviev, Igor .

VP Vibroengineering Procedia. Vol. 25 Kaunas, Lithuania : JVE International Ltd., 2019. p. 128-134 20698 (VP Vibroengineering Procedia; Vol. 25).

Research output

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T1 - On a method of applied symbolic dynamics for investigation of dynamical systems

AU - Ampilova, Natalia

AU - Soloviev, Igor

PY - 2019/6/25

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N2 - We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.

AB - We consider a method of applied symbolic dynamics which may be used to obtain wide spectrum of characteristics of complex dynamical systems: approximation of invariant sets, estimation of topological entropy and approximation of invariant measures. The method has received wide acceptance in studying complex dynamical systems. The main idea of the method is to describe the system behaviour approximately by means of an oriented graph (called symbolic image). Such a graph is a representation of symbolic dynamical system which is more appropriately known as topological Markov chain. There exists a correspondence between trajectories of a given system and paths on the graph, which allows us to design algorithms for estimation of topological entropy, approximate invariant measures of a given system by using stationary flows on the graph and calculate corresponding metric entropies. These values characterize complex behaviour of dynamical systems such as the existence of trajectories with large periods and chaotic regimes. The results of experiments are given for systems with chaotic dynamics.

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KW - invariant measure

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M3 - Conference contribution

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T3 - VP Vibroengineering Procedia

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BT - VP Vibroengineering Procedia

PB - JVE International Ltd.

CY - Kaunas, Lithuania

ER -

Ampilova N, Soloviev I. On a method of applied symbolic dynamics for investigation of dynamical systems. In VP Vibroengineering Procedia. Vol. 25. Kaunas, Lithuania: JVE International Ltd. 2019. p. 128-134. 20698. (VP Vibroengineering Procedia). https://doi.org/10.21595/vp.2019.20698