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Source publication
From a theoretical equation, modeling the dynamic of the time-dependent coefficients of the first and the second Karhunen-Loeve (KL) expansion of a superconducting quantum interference device (SQUID) signal, chaotic phase transition has been studied in the human brain. Through numerical investigations, the bifurcation diagram and the dynamic of Lya...
Contexts in source publication
Context 1
... addition to the above diagrams, we present the 2D phase portrait (x, y) of the KL given by Figure 3 for Ω ¼ 15 with the parameters of Figure 2. ...
Citations
... Nonlinear dynamical methods provide a means for understanding the underlying brain processes in EEG signals and assessing their physiological connotations. One feature of nonlinear dynamical systems is "chaos", which is well suited for the exploration of biological time series, such as heart rates, respiratory records, and particularly EEG [10][11][12]. The theory of nonlinear dynamical systems and chaos theory address deterministic systems that display complex and seemingly random behaviors [9]. ...
(1) Background: Chaos, a feature of nonlinear dynamical systems, is well suited for exploring biological time series, such as heart rates, respiratory records, and particularly electroencephalograms. The primary purpose of this article is to review recent studies using chaos theory and nonlinear dynamical methods to analyze human performance in different brain processes. (2) Methods: Several studies have examined chaos theory and related analytical tools for describing brain dynamics. The present study provides an in-depth analysis of the computational methods that have been proposed to uncover brain dynamics. (3) Results: The evidence from 55 articles suggests that cognitive function is more frequently assessed than other brain functions in studies using chaos theory. The most frequently used techniques for analyzing chaos include the correlation dimension and fractal analysis. Approximate, Kolmogorov and sample entropy account for the largest proportion of entropy algorithms in the reviewed studies. (4) Conclusions: This review provides insights into the notion of the brain as a chaotic system and the successful use of nonlinear methods in neuroscience studies. Additional studies of brain dynamics would aid in improving our understanding of human cognitive performance.
