Phase shifts inside Arnold tongues of weakly coupled oscillators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00140742" target="_blank" >RIV/00216224:14310/25:00140742 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.cnsns.2025.108729" target="_blank" >https://doi.org/10.1016/j.cnsns.2025.108729</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cnsns.2025.108729" target="_blank" >10.1016/j.cnsns.2025.108729</a>
Alternative languages
Result language
angličtina
Original language name
Phase shifts inside Arnold tongues of weakly coupled oscillators
Original language description
In this paper, we investigate phase synchronization phenomena in weakly coupled oscillators, with a particular focus on the phase shifts that occur within Arnold tongues. Using a proposed theoretical approach, we provide proof of the existence of the corresponding cycle manifold near zero coupling, along with a detailed derivation of its shape. This allows us to explore the conditions under which phase-shift synchronization arises. We employ the implicit function theorem in an appropriate Banach space to establish the existence of the cycle manifold and provide a methodology to study in-phase and anti-phase synchrony in systems governed by both ordinary and delay differential equations. We introduce a numerical technique for cycle continuation that reveals the shift structure of Arnold tongues in coupling and parameter space near the cusps, offering new insights into the dynamics of phase-shifted coupled oscillators. This framework is applied to a classic model of two coupled circle oscillators, coupled van der Pol oscillators, a model of two interneurons, and a two-level interneuronal network to better understand and demonstrate the numerical continuation methodology, which allows for the study of phase synchronization in neuroscience and other fields. The proposed methods not only advance the theoretical understanding of synchronization but also offer practical computational tools for studying complex oscillatory systems.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Nonlinear Science and Numerical Simulation
ISSN
1007-5704
e-ISSN
1878-7274
Volume of the periodical
145
Issue of the periodical within the volume
June
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
22
Pages from-to
1-22
UT code for WoS article
001441575300001
EID of the result in the Scopus database
2-s2.0-85219498491