Phase shifts inside Arnold tongues of weakly coupled oscillators

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Phase shifts inside Arnold tongues of weakly coupled oscillators

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Phase shifts inside Arnold tongues of weakly coupled oscillators

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Communications in Nonlinear Science and Numerical Simulation

ISSN

1007-5704

e-ISSN

1878-7274

Svazek periodika

145

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

1-22

Kód UT WoS článku

001441575300001

EID výsledku v databázi Scopus

2-s2.0-85219498491