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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00132617" target="_blank" >RIV/00216224:14310/23:00132617 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/ICAMCS59110.2023.00009" target="_blank" >http://dx.doi.org/10.1109/ICAMCS59110.2023.00009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/ICAMCS59110.2023.00009" target="_blank" >10.1109/ICAMCS59110.2023.00009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

2023 International Conference on Applied Mathematics & Computer Science (ICAMCS)

ISBN

9798350324266

ISSN

—

e-ISSN

—

Počet stran výsledku

9

Strana od-do

1-9

Název nakladatele

IEEE Computer Society Conference Publishing Services (CPS)

Místo vydání

USA

Místo konání akce

Lefkada, Řecko

Datum konání akce

8. 8. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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