Causality, Dynamical Systems and the Arrow of Time

0491998 - ÚI 2019 RIV US eng J - Journal Article
Paluš, Milan - Krakovská, A. - Jakubík, J. - Chvosteková, M.
Causality, Dynamical Systems and the Arrow of Time.
Chaos. Roč. 28, č. 7 (2018), č. článku 075307. ISSN 1054-1500. E-ISSN 1089-7682
R&D Projects: GA MZd(CZ) NV15-33250A
Grant - others:Slovak Grant Agency(SK) 2/0011/16; Slovak Development Agency(SK) APVV-15-0295
Institutional support: RVO:67985807
Keywords : causality * electroencephalography * directed coherence * cardiovascular-system * strange attractors * nonlinearity * synchronization * predictability * oscillators * temperature
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 2.643, year: 2018

Using several methods for detection of causality in time series, we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. We illustrate these findings in causality detected in experimental time series from the climate system and mammalian cardio-respiratory interactions. Any scientific discipline strives to explain causes of observed phenomena. Studying phenomena evolving in time and providing measurable quantities which can be registered in consecutive instants of time and stored in datasets called time series brings researchers a possibility to apply modern mathematical methods which can detect possible causal relations between different datasets. Methods based on the so-called Granger causality have been applied in diverse scientific fields from economics and finance, through Earth and climate sciences to research trying to understand the human brain. Chaotic dynamical systems are mathematical models reflecting very complicated behaviour. Recently, cooperative phenomena have been observed in coupled chaotic systems due to their ability to synchronize. On the way to synchronization, the question which system influences other systems emerges. To answer this question, research works successfully applied the Granger causality methods. In this study, we demonstrate that chaotic dynamical systems do not respect the principle of the effect following the cause. We explain, however, that such principle violation cannot occur in nature, only in mathematical models which, on the other hand, can help us to understand the mechanisms behind the experimentally observed causalities.
Permanent Link: http://hdl.handle.net/11104/0285592