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Transient chaos and periodic structures in a model of neuronal early afterdepolarization.
Chaos
January 2025
Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Santa Catarina, Brazil.
The presence of chaos is ubiquitous in mathematical models of neuroscience. In experimental neural systems, chaos was convincingly demonstrated in membranes, neurons, and small networks. However, its effects on the brain have long been debated.
View Article and Find Full Text PDFDynamical properties of the composed Logistic-Gauss map.
Chaos
January 2025
Physics Institute, University of São Paulo-USP, São Paulo, SP 05508-090, Brazil.
This study focuses on the analysis of a unique composition between two well-established models, known as the Logistic-Gauss map. The investigation cohesively transitions to an exploration of parameter space, essential for unraveling the complexity of dissipative mappings and understanding the intricate relationships between periodic structures and chaotic regions. By manipulating control parameters, our approach reveals intriguing patterns, with findings enriched by extreme orbits, trajectories that connect local maximum and minimum values of one-dimensional maps.
View Article and Find Full Text PDFThe topology of a chaotic attractor in the Kuramoto-Sivashinsky equation.
Chaos
January 2025
Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a chaotic attractor in a partial differential equation (PDE) is less than three, even though that attractor is embedded within an infinite-dimensional space. Here, we study the Kuramoto-Sivashinsky PDE at the onset of chaos.
View Article and Find Full Text PDFChaotic recurrent neural networks for brain modelling: A review.
Neural Netw
December 2024
Institute of Cognitive Sciences and Technology, National Research Council, Via Romagnosi 18a, I-00196, Rome, Italy.
Even in the absence of external stimuli, the brain is spontaneously active. Indeed, most cortical activity is internally generated by recurrence. Both theoretical and experimental studies suggest that chaotic dynamics characterize this spontaneous activity.
View Article and Find Full Text PDFEffect of competition on emergent phases and phase transitions in competitive systems.
Theor Popul Biol
February 2025
School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, PR China.
This paper considers Lotka-Volterra competitive systems characterizing laboratory experiment by Hu et al. (Science, 378:85-89, 2022). Using dynamical systems theory and projection method, we give theoretical analysis and numerical simulation on the model with four species by demonstrating equilibrium stability, periodic oscillation and chaotic fluctuation in the systems.
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