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Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci.
View Article and Find Full Text PDFSymbolic dynamics of joint brain states during dyadic coordination.
Chaos
January 2025
Department of Cognitive Sciences, University of California, Irvine, California 92617, USA.
We propose a novel approach to investigate the brain mechanisms that support coordination of behavior between individuals. Brain states in single individuals defined by the patterns of functional connectivity between brain regions are used to create joint symbolic representations of brain states in two or more individuals to investigate symbolic dynamics that are related to interactive behaviors. We apply this approach to electroencephalographic data from pairs of subjects engaged in two different modes of finger-tapping coordination tasks (synchronization and syncopation) under different interaction conditions (uncoupled, leader-follower, and mutual) to explore the neural mechanisms of multi-person motor coordination.
View Article and Find Full Text PDFDirected recurrence networks for the analysis of nonlinear and complex dynamical systems.
Chaos
January 2025
Department of Management Science and Technology, Tohoku University, Sendai 980-8579, Japan.
Complex network approaches have been emerging as an analysis tool for dynamical systems. Different reconstruction methods from time series have been shown to reveal complicated behaviors that can be quantified from the network's topology. Directed recurrence networks have recently been suggested as one such method, complementing the already successful recurrence networks and expanding the applications of recurrence analysis.
View Article and Find Full Text PDFReconstructing attractors with autoencoders.
Chaos
January 2025
IMAS-CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
We propose a method based on autoencoders to reconstruct attractors from recorded footage, preserving the topology of the underlying phase space. We provide theoretical support and test the method with (i) footage of the temperature and stream function fields involved in the Lorenz atmospheric convection problem and (ii) a time series obtained by integrating the Rössler equations.
View Article and Find Full Text PDFKoopman learning with episodic memory.
Chaos
January 2025
AIMdyn, Inc., Santa Barbara, California 93101, USA.
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to traditional machine learning methodologies, make Koopman learning an especially appealing approach. Despite this, little work has been performed on endowing Koopman learning with the ability to leverage its own failures.
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