PŘIBYLOVÁ, Lenka. Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms. In International Conference on Applied Mathematics & Computer Science Lefkada Island, Greece. August 8-10, 2023. 2023.
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Original name Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms
Name in Czech Zkoumání mechanismů synchronizace prostřednictvím bifurkační analýzy - jednotný přístup napříč neuronální, ekologickou a fyzikální oblastí
Name (in English) Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms
Authors PŘIBYLOVÁ, Lenka.
Edition International Conference on Applied Mathematics & Computer Science Lefkada Island, Greece. August 8-10, 2023, 2023.
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Type of outcome Presentations at conferences
Confidentiality degree is not subject to a state or trade secret
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Keywords (in Czech) synchronizace, Morrisové-Lecarův model neuronu, model Josephsonova přechodu buzeného střídavým proudem, model dravec-kořist se sezónním Alleeho efektem, bifurkace vzniku toru, bifurkace limitního bodu cyklu, struktura Arnoldova jazyku
Keywords in English synchronization, Morris-Lecar neuron model, AC-driven Josephson junction model, predator-prey model with seasonal Allee effect, torus bifurcation, limit point of cycle bifurcation, Arnold tongue structure
Tags International impact
Changed by Changed by: doc. RNDr. Lenka Přibylová, Ph.D., učo 9607. Changed: 13/10/2023 09:59.
Abstract
Synchronization mechanisms are crucial to many dynamical systems, from networks of neurons to physical dynamical systems like superconductive junctions. We introduce a unified method focusing on bifurcation theory tools like Arnold tongues and cycle manifolds on tori using the continuation program MatCont.This approach can elucidate synchronization scenarios in various dynamical systems. We highlight bistability in the synchronization patterns of coupled neurons, which might be linked to very high-frequency EEG signals near epileptic foci. Although this connection remains unconfirmed, it offers insights into pathological brain activity. Furthermore, we demonstrate our method's efficacy in analyzing Shapiro steps in superconductive junctions and seasonal synchronization in population models. This underscores its broad applicability, encouraging further use and adaptation of this approach in understanding synchronization across diverse systems.
Links
MUNI/A/1132/2022, interní kód MUName: Matematické a statistické modelování 7
Investor: Masaryk University
MUNI/G/1213/2022, interní kód MUName: Mathematical modeling of very and ultra-fast oscillations in EEG signals
Investor: Masaryk University, Mathematical modeling of very and ultra-fast oscillations in EEG signals, INTERDISCIPLINARY - Interdisciplinary research projects
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