Nonlinear DynamicsPub Date : 2024-01-01Epub Date: 2024-08-15DOI: 10.1007/s11071-024-10026-x
George Haller, Bálint Kaszás
{"title":"Data-driven linearization of dynamical systems.","authors":"George Haller, Bálint Kaszás","doi":"10.1007/s11071-024-10026-x","DOIUrl":"10.1007/s11071-024-10026-x","url":null,"abstract":"<p><p>Dynamic mode decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly in others, a clarification of the assumptions under which DMD is applicable is desirable. Upon closer inspection, existing interpretations of DMD methods based on the Koopman operator are not quite satisfactory: they justify DMD under assumptions that hold only with probability zero for generic observables. Here, we give a justification for DMD as a local, leading-order reduced model for the dominant system dynamics under conditions that hold with probability one for generic observables and non-degenerate observational data. We achieve this for autonomous and for periodically forced systems of finite or infinite dimensions by constructing linearizing transformations for their dominant dynamics within attracting slow spectral submanifolds (SSMs). Our arguments also lead to a new algorithm, data-driven linearization (DDL), which is a higher-order, systematic linearization of the observable dynamics within slow SSMs. We show by examples how DDL outperforms DMD and EDMD on numerical and experimental data.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s11071-024-10026-x.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"112 21","pages":"18639-18663"},"PeriodicalIF":5.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11362512/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142110570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nonlinear DynamicsPub Date : 2024-01-01Epub Date: 2024-08-16DOI: 10.1007/s11071-024-10068-1
Murad Banaji, Balázs Boros, Josef Hofbauer
{"title":"Bifurcations in planar, quadratic mass-action networks with few reactions and low molecularity.","authors":"Murad Banaji, Balázs Boros, Josef Hofbauer","doi":"10.1007/s11071-024-10068-1","DOIUrl":"10.1007/s11071-024-10068-1","url":null,"abstract":"<p><p>In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity. We fully characterise generic bifurcations of positive equilibria in such networks with up to four reactions, and product molecularity no higher than three. In these networks we find fold, Andronov-Hopf, Bogdanov-Takens and Bautin bifurcations, and prove the non-occurrence of any other generic bifurcations of positive equilibria. In addition, we present a number of results which go beyond planar, quadratic networks. For example, we show that mass-action networks without conservation laws admit no bifurcations of codimension greater than <math><mrow><mi>m</mi> <mo>-</mo> <mn>2</mn></mrow> </math> , where <i>m</i> is the number of reactions; we fully characterise quadratic, rank-one mass-action networks admitting fold bifurcations; and we write down some necessary conditions for Andronov-Hopf and cusp bifurcations in mass-action networks. Finally, we draw connections with a number of previous results in the literature on nontrivial dynamics, bifurcations, and inheritance in mass-action networks.</p>","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"112 23","pages":"21425-21448"},"PeriodicalIF":5.7,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11466909/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142471843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lump solution, interaction solution, and interference wave for the (3+1)-dimensional BKP-Boussinesq equation as well as analysis of BNNM model degradation","authors":"Yuanlin Liu, Zhimin Ma, Ruoyang Lei","doi":"10.1007/s11071-023-09169-0","DOIUrl":"https://doi.org/10.1007/s11071-023-09169-0","url":null,"abstract":"","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":" 30","pages":""},"PeriodicalIF":5.6,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139141575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fei Yu, Ye Yuan, Chaoran Wu, Wei Yao, Cong Xu, Shuo Cai, Chunhua Wang
{"title":"Modeling and hardware implementation of a class of Hamiltonian conservative chaotic systems with transient quasi-period and multistability","authors":"Fei Yu, Ye Yuan, Chaoran Wu, Wei Yao, Cong Xu, Shuo Cai, Chunhua Wang","doi":"10.1007/s11071-023-09148-5","DOIUrl":"https://doi.org/10.1007/s11071-023-09148-5","url":null,"abstract":"","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":" 24","pages":""},"PeriodicalIF":5.6,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139138635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asynchronous rate anti-bump switching convex control for a class of switched positive linear systems","authors":"Shuoyang Hu, Ruihua Wang, Shumin Fei","doi":"10.1007/s11071-023-09175-2","DOIUrl":"https://doi.org/10.1007/s11071-023-09175-2","url":null,"abstract":"","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":" 43","pages":""},"PeriodicalIF":5.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139144522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Detection method of ship-radiated noise based on fractional-order dual coupling oscillator","authors":"Guohui Li, Ruiting Xie, Hong Yang","doi":"10.1007/s11071-023-09150-x","DOIUrl":"https://doi.org/10.1007/s11071-023-09150-x","url":null,"abstract":"","PeriodicalId":19723,"journal":{"name":"Nonlinear Dynamics","volume":"8 7","pages":""},"PeriodicalIF":5.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139148036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}