TY  - JOUR
AU  - Maletić, Slobodan
AU  - Zhao, Yi
AU  - Rajković, Milan
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1115
AB  - Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network. Published by AIP Publishing.
T2  - Chaos
T1  - Persistent topological features of dynamical systems
VL  - 26
IS  - 5
DO  - 10.1063/1.4949472
ER  - 

@article{
author = "Maletić, Slobodan and Zhao, Yi and Rajković, Milan",
year = "2016",
abstract = "Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network. Published by AIP Publishing.",
journal = "Chaos",
title = "Persistent topological features of dynamical systems",
volume = "26",
number = "5",
doi = "10.1063/1.4949472"
}

Maletić, S., Zhao, Y.,& Rajković, M.. (2016). Persistent topological features of dynamical systems. in Chaos, 26(5).
https://doi.org/10.1063/1.4949472

Maletić S, Zhao Y, Rajković M. Persistent topological features of dynamical systems. in Chaos. 2016;26(5).
doi:10.1063/1.4949472 .

Maletić, Slobodan, Zhao, Yi, Rajković, Milan, "Persistent topological features of dynamical systems" in Chaos, 26, no. 5 (2016),
https://doi.org/10.1063/1.4949472 . .