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@proceedings{2324062,
author = {Přibylová, Lenka},
booktitle = {International Conference on Applied Mathematics & Computer Science Lefkada Island, Greece. August 8-10, 2023},
keywords = {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},
title = {Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms},
url = {https://youtu.be/Kkk__KhqaoE},
year = {2023}
}
TY - CONF
ID - 2324062
AU - Přibylová, Lenka
PY - 2023
TI - Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms
KW - 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
UR - https://youtu.be/Kkk__KhqaoE
N2 - 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.
ER -
PŘIBYLOVÁ, Lenka. Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms. In \textit{International Conference on Applied Mathematics \&{} Computer Science Lefkada Island, Greece. August 8-10, 2023}. 2023.
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