Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
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 (Vibroengineering Procedia).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
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TY - GEN
T1 - On a method of applied symbolic dynamics for investigation of dynamical systems
AU - Ampilova, Natalia
AU - Soloviev, Igor
N1 - Conference code: 39
PY - 2019/6/1
Y1 - 2019/6/1
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.
KW - dynamical systems
KW - applied symbolic dynamics
KW - topological entropy
KW - symbolic image
KW - invariant measure
KW - Applied symbolic dynamics
KW - Invariant measure
KW - Topological entropy
KW - Symbolic image
KW - Dynamical systems
UR - http://www.scopus.com/inward/record.url?scp=85069481001&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/method-applied-symbolic-dynamics-investigation-dynamical-systems
U2 - 10.21595/vp.2019.20698
DO - 10.21595/vp.2019.20698
M3 - Conference contribution
VL - 25
T3 - Vibroengineering Procedia
SP - 128
EP - 134
BT - VP Vibroengineering Procedia
PB - JVE International Ltd.
CY - Kaunas, Lithuania
T2 - 39th International JVE Conference
Y2 - 25 June 2019 through 26 June 2019
ER -
ID: 43568410