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A family of coexisting multi-scroll chaos and its selected control in coupled non-oscillatory neurons: A case study.
Heliyon
January 2025
Unité de Recherche d'Automatique et d'Informatique Appliquée (UR-AIA), IUT-FV Bandjoun University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
This study presents a family of coexisting multi-scroll chaos in a network of coupled non-oscillatory neurons. The dynamics of the system are analyzed using phase portraits, basins of attraction, time series, bifurcation diagrams, and spectra of Lyapunov exponents. The coexistence of multiple bifurcation diagrams leads to a complex pattern of multi-scroll formation, which is further complicated by the presence of coexisting single-scroll attractors that merge to form multi-scroll chaos.
View Article and Find Full Text PDFSynchronization stability of epileptic brain network with higher-order interactions.
Chaos
January 2025
Beijing Institute of Functional Neurosurgery, Xuanwu Hospital, Capital Medical University, Beijing 100053, China.
Generally, epilepsy is considered as abnormally enhanced neuronal excitability and synchronization. So far, previous studies on the synchronization of epileptic brain networks mainly focused on the synchronization strength, but the synchronization stability has not yet been explored as deserved. In this paper, we propose a novel idea to construct a hypergraph brain network (HGBN) based on phase synchronization.
View Article and Find Full Text PDFTransient 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 PDFReliable detection of directional couplings using cross-vector measures.
Chaos
January 2025
Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana, Slovenia.
Detecting directional couplings from time series is crucial in understanding complex dynamical systems. Various approaches based on reconstructed state-spaces have been developed for this purpose, including a cross-distance vector measure, which we introduced in our recent work. Here, we devise two new cross-vector measures that utilize ranks and time series estimates instead of distances.
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.
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