Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Exploring Synchronization Mechanisms via Bifurcation Analysis – A Unified Approach Across Neuronal, Ecological and Physical Realms
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
2023 International Conference on Applied Mathematics & Computer Science (ICAMCS)
ISBN
9798350324266
ISSN
—
e-ISSN
—
Number of pages
9
Pages from-to
1-9
Publisher name
IEEE Computer Society Conference Publishing Services (CPS)
Place of publication
USA
Event location
Lefkada, Řecko
Event date
Aug 8, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—