https://m2.mtmt.hu/ hun 2026-05-02 15:38 JournalArticle 35600391 VALIDATED true First published online: 11 November 2024 Correspondence Address: Beregi, S.; Department of Infectious Disease Epidemiology, United Kingdom; email: s.beregi@imperial.ac.uk Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, NKFIH-PD-146459 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH Funding details: Medical Research Council, MRC, MR/X020258/1 Funding details: Medical Research Council, MRC Funding text 1: This work was supported by the Hungarian National Research, Development and Innovation Office (Henrik T Sykora: NKFIH-PD-146459) and the MRC Centre for Global Infectious Disease Analysis funded by the UK Medical Research Council (MRC) (Sandor Beregi: MR/X020258/1). 0 false 2026-04-27T07:43:41.602+0000 2025-04-07T07:17:17.747+0000 2024-11-25T14:56:35.121+0000 true 10072271 Andódy Katalin /api/admin/10072271 Admin Andódy Katalin (BME admin4) true 2025-04-07T07:17:18.786+0000 2025-04-07T07:17:18.786+0000 2025-04-07T07:16:01.636+0000 true 10072271 Andódy Katalin /api/admin/10072271 Admin Andódy Katalin (BME admin4) true true false true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Szakcikk (Folyóiratcikk) 101 true 10000059 true 1 /api/category/1 Category Tudományos true 1 Sykora, Henrik T. true true /api/journal/14303 REVIEWED NONLINEAR DYNAMICS 0924-090X 1573-269X true false 14303 false 14303 true 0924-090X 1573-269X Journal FOREIGN 113 8 8249 8263 8249 15 2025 Noise limits the information that can be experimentally extracted from dynamical systems. In this study, we review the Control-based Continuation (CBC) approach, which is commonly used for experimental characterisation of nonlinear systems with coexisting stable and unstable steady states. The CBC technique, however, uses a deterministic framework, whereas in practice, almost all measurements are subject to some level of random perturbation, and the underlying dynamical system is inherently noisy. In order to discover what the CBC is capable of extracting from inherently noisy experiments, we study the Hopf normal form with quintic terms with additive noise. The bifurcation diagram of the deterministic core of this system is well-known, therefore the discrepancies introduced by noise can be easily assessed. First, we utilise the Step-Matrix Multiplication based Path Integral (SMM-PI) method to approximate the system’s steady state probability density function (PDF) for different intensity noise perturbations. We associate the local extrema of the resulting PDFs with limit cycles, and compare the resulting bifurcation diagram to those captured by CBC. We show that CBC estimates the bifurcation diagram of the noisy system well for noise intensities varying from small to moderate, and in practice, the amplitudes provided by CBC may be accepted as a ’best guess’ proxy for the vibration amplitudes characteristic to the near periodic solutions in a wide range of experiments. © The Author(s) 2024. true 2024 true true true false true false GOLD 2026-04-27 true https://doi.org/10.1007/s11071-024-10522-0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 5 5 Folyóiratcikk Journal Article 24 1 Könyvrészlet Chapter in Book 25 0 Könyv Book 23 0 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 0 Egyéb Miscellaneous 29 0 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2025 0 1 1 1 1 Q1 false false false false 2025-01-27T14:17:36.527+0000 Műszaki Mechanikai Tanszék (BME / GPK) 2 5 1 2 0 true Language 10002 /api/language/10002 Angol Angol English true 2 true PersonAuthorship 121841199 /api/authorship/121841199 Sykora, Henrik T. [Sykora, Henrik Tamás (Műszaki mechanika), szerző] Műszaki Mechanikai Tanszék (BME / GPK) 1 0.5 true false false Author 10053835 /api/author/10053835 Sykora Henrik Tamás (Műszaki mechanika) Sykora Henrik Tamás true 10053835 true Sykora Henrik T. true false false AuthorshipType 1 /api/authorshiptype/1 Szerző 0 true 0 true false true PersonAuthorship 121841200 /api/authorship/121841200 Beregi, Sandor ✉ [Beregi, Sándor (műszaki mechanika), szerző] 2 0.5 false true true Author 10049622 /api/author/10049622 Beregi Sándor (műszaki mechanika) Beregi Sándor true 10049622 true Beregi Sandor true false false AuthorshipType 1 /api/authorshiptype/1 Szerző 0 true 0 true false true PublicationIdentifier 28008701 /api/publicationidentifier/28008701 DOI: 10.1007/s11071-024-10522-0 PlainSource 6 /api/publicationsource/6 DOI PublicationSourceType 10001 /api/publicationsourcetype/10001 DOI true true true DOI DOI https://doi.org/@@@ true true 6 true GOLD true IDENTICAL 10.1007/s11071-024-10522-0 https://doi.org/10.1007/s11071-024-10522-0 false true PublicationIdentifier 28008702 /api/publicationidentifier/28008702 WoS: 001352507700001 PlainSource 1 /api/publicationsource/1 WoS PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 001352507700001 https://www.webofscience.com/wos/woscc/full-record/001352507700001 false true PublicationIdentifier 29196777 /api/publicationidentifier/29196777 Scopus: 105001074275 PlainSource 3 /api/publicationsource/3 Scopus PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true 105001074275 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001074275 false true Classification 10807 /api/classification/10807 Műszaki és technológiai tudományok true true Keyword 6052 /api/keyword/6052 Probability density function true 6052 true Keyword 1013991 /api/keyword/1013991 Matrix algebra true 1013991 true Keyword 1014034 /api/keyword/1014034 Perturbation techniques true 1014034 true Keyword 1030682 /api/keyword/1030682 nonlinear dynamical systems true 1030682 true Keyword 1030684 /api/keyword/1030684 stochastic systems true 1030684 true Keyword 1066006 /api/keyword/1066006 Bifurcation diagram true 1066006 true Keyword 1066006 /api/keyword/1066006 Bifurcation diagram true 1066006 true Keyword 1066178 /api/keyword/1066178 Stochastic control systems true 1066178 true Keyword 1102632 /api/keyword/1102632 Vibration analysis true 1102632 true Keyword 1132756 /api/keyword/1132756 Hopf bifurcation true 1132756 true Keyword 1162339 /api/keyword/1162339 Subcritical Hopf bifurcation true 1162339 true Keyword 1162339 /api/keyword/1162339 Subcritical Hopf bifurcation true 1162339 true Keyword 1351895 /api/keyword/1351895 MATRIX MULTIPLICATION true 1351895 true Keyword 1541265 /api/keyword/1541265 Deterministics true true Keyword 1658376 /api/keyword/1658376 path integral method true true Keyword 1714579 /api/keyword/1714579 Control-based continuation true true Keyword 2136329 /api/keyword/2136329 stochastics true true Keyword 3661747 /api/keyword/3661747 Control-based continuation (CBC) true true Keyword 3661748 /api/keyword/3661748 Noisy systems true true Keyword 3661749 /api/keyword/3661749 Step-matrix multiplication path integral (SMM-PI) method true true Keyword 3661750 /api/keyword/3661750 Bi-stable oscillators true true Keyword 3661751 /api/keyword/3661751 Noisy system true true Keyword 3661752 /api/keyword/3661752 Step-matrix multiplication path integral method true true SjrRating 11552582 /api/sjrrating/11552582 sjr:Q1 (2025) Scopus - Aerospace Engineering NONLINEAR DYNAMICS 0924-090X 1573-269X 17 0.24 journal RatingType 10002 /api/ratingtype/10002 sjr sjr true true ClassificationExternal 2202 /api/classificationexternal/2202 Scopus - Aerospace Engineering true 2202 true Q1 DIRECT true true Reference 60198875 /api/reference/60198875 1. 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Renson, L., Sieber, J., Barton, D.A.W., Shaw, A.D., Neild, S.A., Numerical continuation in nonlinear experiments using local Gaussian process regression (2019) Nonlinear Dyn, 98 (4), pp. 2811-2826 41 false true /api/publication/35600391 Sykora Henrik T. et al. From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method. (2025) NONLINEAR DYNAMICS 0924-090X 1573-269X 113 8 8249-8263<div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10053835"><a href="/gui2/?type=authors&mode=browse&sel=10053835" target="_blank">Sykora Henrik T. (<span class="authorship-author-name">Sykora Henrik Tamás</span> <span class="authorAux-mtmt"> Műszaki mechanika</span>) </a> </span> <span class="author-affil"><span title="Budapesti Műszaki és Gazdaságtudományi Egyetem">BME</span>/<span title="Gépészmérnöki Kar">GPK</span>/Műszaki Mechanikai Tanszék</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10049622"><a href="/gui2/?type=authors&mode=browse&sel=10049622" target="_blank">Beregi Sandor ✉ (<span class="authorship-author-name">Beregi Sándor</span> <span class="authorAux-mtmt"> műszaki mechanika</span>) </a> </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;35600391" target="_blank">From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method</a></div> <div> <span class="journal-title">NONLINEAR DYNAMICS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0924-090X">0924-090X</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1573-269X">1573-269X</a>)</span>: <span class="journal-volume">113</span> <span class="journal-issue">8</span> <span class="page"> pp 8249-8263 </span> <span class="year">(2025)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_GOLD" title=" Gold "> <a style="color:blue" title="10.1007/s11071-024-10522-0" target="_blank" href="https://doi.org/10.1007/s11071-024-10522-0"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="001352507700001" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/001352507700001"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="105001074275" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001074275"> Scopus </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Aerospace Engineering&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Applied Mathematics&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Control and Systems Engineering&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Electrical and Electronic Engineering&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mechanical Engineering&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Ocean Engineering&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 1</span> | Független: 1 | Függő: 0 | Nem jelölt: 0 | WoS jelölt: 1 | Scopus jelölt:&nbsp;1 | WoS/Scopus jelölt:&nbsp;1 | DOI jelölt:&nbsp;1 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;35600391&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 5 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 35600391</span> | <span class="status-data status-VALIDATED"> Egyeztetett </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2025.04.07. 09:17 Andódy Katalin (BME admin4) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: First published online: 11 November 2024 Correspondence Address: Beregi, S.; Department of Infectious Disease Epidemiology, United Kingdom; email: s.beregi@imperial.ac.uk Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, NKFIH-PD-146459 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH ...</pre> </div></div>