Exploring Synchronization Mechanisms via Bifurcation Analysis –
A Unified Approach Across Neuronal, Ecological and Physical
Realms

D 2024

Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms

PŘIBYLOVÁ, Lenka

Základní údaje

Originální název

Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms

Autoři

PŘIBYLOVÁ, Lenka (203 Česká republika, garant, domácí)

Vydání

2024. vyd. Greece, 2023 International Conference on Applied Mathematics & Computer Science (ICAMCS), od s. 1-9, 9 s. 2024

Nakladatel

IEEE

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10102 Applied mathematics

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL URL

Organizační jednotka

Přírodovědecká fakulta

ISBN

979-8-3503-2427-3

DOI

http://dx.doi.org/10.1109/ICAMCS59110.2023

Klíčová slova anglicky

synchronization; Morris–Lecar model; AC-driven Josephson junction model; predator-prey model with seasonal Allee effect; torus bifurcation; limit point of cycle bifurcation; Arnold tongue structure

Štítky

Arnold tongues, bifurcation, Limit cycle, synchronization

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 21. 2. 2024 10:00, doc. RNDr. Lenka Přibylová, Ph.D.

Anotace

V originále

Synchronization mechanisms, while inherently complex, are central to a wide range of dynamical systems, from neuronal networks to physical systems like superconductive junctions. The aim of this contribution is to introduce a unified approach using the continuation program, MatCont, to explore these phenomena through the lens of bifurcation theory, specifically employing Arnold tongues and limit points of cycle manifolds on tori as analytical tools. Our findings suggest that this approach may explain the synchronization scenarios in various fields. Firstly, we focus on networks of neurons connected by gap-junctions, which can be modeled as neurons excited by external alternating currents or by interconnected neurons. Whether addressing a single neuron or a complex network, our approach provides a comprehensive understanding of the possible synchronization scenarios. This methodology is also applied to shed light on bistability observed in in-phase and anti-phase synchronization patterns in neuronal networks. Our research proposes an explanation that these patterns could be linked to very high-frequency EEG signals observed near epileptic foci. While the definitive connection between these bistable synchronization patterns and very high-frequency oscillations is yet to be established, our methodology offers a promising direction for investigation, potentially contributing to a deeper understanding of pathological brain activity. Further demonstrating the applicability of our approach, we present its successful implementation in deciphering Shapiro steps in superconductive Josephson junctions and seasonal synchronization in population models. These applications underscore the power of our methodology not only in neuroscience but also in the broader context of complex dynamical systems. Through the exposition of this MatCont-based method for bifurcation analysis, we aim to inspire further utilization and development of this approach, catalyzing advancements in modeling and understanding synchronization mechanisms across a diverse range of systems.

Návaznosti

MUNI/A/1132/2022, interní kód MU

Název: Matematické a statistické modelování 7

Investor: Masarykova univerzita, Matematické a statistické modelování 7

MUNI/G/1213/2022, interní kód MU

Název: Mathematical modeling of very and ultra-fast oscillations in EEG signals

Investor: Masarykova univerzita, Mathematical modeling of very and ultra-fast oscillations in EEG signals, INTERDISCIPLINARY - Mezioborové výzkumné projekty

Citovat

PŘIBYLOVÁ, Lenka. Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms. Online. In Nikos Mastorakis. 2023 International Conference on Applied Mathematics & Computer Science (ICAMCS). 2024. vyd. Greece: IEEE, 2024, s. 1-9. ISBN 979-8-3503-2427-3. Dostupné z: https://dx.doi.org/10.1109/ICAMCS59110.2023.

@inproceedings{2376693,
   author = {Přibylová, Lenka},
   address = {Greece},
   booktitle = {2023 International Conference on Applied Mathematics & Computer Science (ICAMCS)},
   doi = {http://dx.doi.org/10.1109/ICAMCS59110.2023},
   edition = {2024},
   editor = {Nikos Mastorakis},
   keywords = {synchronization; Morris–Lecar model; AC-driven Josephson junction model; predator-prey model with seasonal Allee effect; torus bifurcation; limit point of cycle bifurcation; Arnold tongue structure},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Greece},
   isbn = {979-8-3503-2427-3},
   pages = {1-9},
   publisher = {IEEE},
   title = {Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms},
   url = {https://ieeexplore.ieee.org/servlet/opac?punumber=10438514},
   year = {2024}
}

TY  - JOUR
ID  - 2376693
AU  - Přibylová, Lenka
PY  - 2024
TI  - Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms
PB  - IEEE
CY  - Greece
SN  - 9798350324273
KW  - synchronization
KW  - Morris–Lecar model
KW  - AC-driven Josephson junction model
KW  - predator-prey model with seasonal Allee effect
KW  - torus bifurcation
KW  - limit point of cycle bifurcation
KW  - Arnold tongue structure
UR  - https://ieeexplore.ieee.org/servlet/opac?punumber=10438514
N2  - Synchronization mechanisms, while inherently complex, are central to a wide range of dynamical systems, from neuronal networks to physical systems like superconductive junctions. The aim of this contribution is to introduce a unified approach using the continuation program, MatCont, to explore these phenomena through the lens of bifurcation theory, specifically employing Arnold tongues and limit points of cycle manifolds on tori as analytical tools. Our findings suggest that this approach may explain the synchronization scenarios in various fields. Firstly, we focus on networks of neurons connected by gap-junctions, which can be modeled as neurons excited by external alternating currents or by interconnected neurons. Whether addressing a single neuron or a complex network, our approach provides a comprehensive understanding of the possible synchronization scenarios. This methodology is also applied to shed light on bistability observed in in-phase and anti-phase synchronization patterns in neuronal networks. Our research proposes an explanation that these patterns could be linked to very high-frequency EEG signals observed near epileptic foci. While the definitive connection between these bistable synchronization patterns and very high-frequency oscillations is yet to be established, our methodology offers a promising direction for investigation, potentially contributing to a deeper understanding of pathological brain activity. Further demonstrating the applicability of our approach, we present its successful implementation in deciphering Shapiro steps in superconductive Josephson junctions and seasonal synchronization in population models. These applications underscore the power of our methodology not only in neuroscience but also in the broader context of complex dynamical systems. Through the exposition of this MatCont-based method for bifurcation analysis, we aim to inspire further utilization and development of this approach, catalyzing advancements in modeling and understanding synchronization mechanisms across a diverse range of systems.
ER  -

PŘIBYLOVÁ, Lenka. Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms. Online. In Nikos Mastorakis. \textit{2023 International Conference on Applied Mathematics \&{} Computer Science (ICAMCS)}. 2024. vyd. Greece: IEEE, 2024, s.~1-9. ISBN~979-8-3503-2427-3. Dostupné z: https://dx.doi.org/10.1109/ICAMCS59110.2023.

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