Embedding nonlinear systems with two or more harmonic phase terms near the Hopf–Hopf bifurcation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00130030" target="_blank" >RIV/00216224:14310/23:00130030 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s11071-022-07906-5" target="_blank" >https://link.springer.com/article/10.1007/s11071-022-07906-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11071-022-07906-5" target="_blank" >10.1007/s11071-022-07906-5</a>

Result language

angličtina

Original language name

Embedding nonlinear systems with two or more harmonic phase terms near the Hopf–Hopf bifurcation

Original language description

Nonlinear problems involving phases occur ubiquitously throughout applied mathematics andphysics, ranging from neuronal models to the search for elementary particles. The phase variables present in such models usually enter as harmonic terms and, being unbounded, pose an open challenge for studying bifurcations in these systems through standard numerical continuation techniques. Here, we propose to transform and embed the original model equations involving phases into structurally stable generalized systems that are more suitable for analysis via standard predictor–corrector numerical continuation methods. The structural stability of the generalized system is achieved by replacing each harmonic term in the original system by a supercritical Hopf bifurcation normal form subsystem. As an illustration of this general approach, specific details are provided for the ac-driven, Stewart–McCumber model of a single Josephson junction. It is found that the dynamics of the junction is underpinned by a two-parameter Hopf–Hopf bifurcation, detected in the generalized system. The Hopf–Hopf bifurcation gives birth to an invariant torus through Neimark–Sacker bifurcation of limit cycles. Continuation of the Neimark–Sacker bifurcation of limit cycles in the two-parameter space provides a complete picture of the overlapping Arnold tongues (regions of frequency-locked periodic solutions), which are in precise agreement with the widths of the Shapiro steps that can be measured along the current–voltage characteristics of the junction at various fixed values of the ac-drive amplitude.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2023

Confidentiality

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

Name of the periodical

Nonlinear Dynamics

ISSN

0924-090X

e-ISSN

1573-269X

Volume of the periodical

111

Issue of the periodical within the volume

2

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

15

Pages from-to

1537-1551

UT code for WoS article

000863219300004

EID of the result in the Scopus database

2-s2.0-85139132624