Physica D: Nonlinear Phenomena最新文献

Periodic orbits and integrability of Rocard’s system

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-03-03 DOI: 10.1016/j.physd.2025.134594

Xinhao Hu, Yilei Tang

引用次数: 0

Automatic classification of magnetic field line topology by persistent homology

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-03-01 DOI: 10.1016/j.physd.2025.134595

N. Bohlsen , V. Robins , M. Hole

{"title":"Automatic classification of magnetic field line topology by persistent homology","authors":"N. Bohlsen , V. Robins , M. Hole","doi":"10.1016/j.physd.2025.134595","DOIUrl":"10.1016/j.physd.2025.134595","url":null,"abstract":"<div><div>A method for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using the Vietoris–Rips persistent homology is presented. The input to the method is the Poincare map orbits of field lines and the output is a separation into three classes: islands, chaotic layers, and invariant tori. The classification is tested numerically for the case of a toy model of a perturbed tokamak represented initially in its geometric coordinates. The persistent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> data is demonstrated to be sufficient to distinguish magnetic islands from the other orbits. When combined with persistent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> information, describing the average spacing between points on the Poincare section, the larger chaotic orbits can then be separated from very thin chaotic layers and invariant tori. It is then shown that if straight field line coordinates exist for a nearby integrable field configuration, the performance of the classification can be improved by transforming into this natural coordinate system. The focus is the application to toroidal magnetic confinement but the method is sufficiently general to apply to generic <span><math><mrow><mn>1</mn><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>d Hamiltonian systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134595"},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Giant vortex in a harmonically-trapped rotating dipolar 164Dy condensate

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-27 DOI: 10.1016/j.physd.2025.134590

Luis E. Young-S. , S.K. Adhikari

引用次数: 0

Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-27 DOI: 10.1016/j.physd.2025.134589

Zhi-Xuan Meng , Shuai-Xia Xu , Yu-Qiu Zhao

引用次数: 0

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-25 DOI: 10.1016/j.physd.2025.134572

Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo

{"title":"Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems","authors":"Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo","doi":"10.1016/j.physd.2025.134572","DOIUrl":"10.1016/j.physd.2025.134572","url":null,"abstract":"<div><div>This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. We demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134572"},"PeriodicalIF":2.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lp stability-based synchronization of delayed multi-weight neural networks under switching topologies

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-22 DOI: 10.1016/j.physd.2025.134577

Yunxiao Jia, Xiaona Yang, Xian Zhang

{"title":"Lp stability-based synchronization of delayed multi-weight neural networks under switching topologies","authors":"Yunxiao Jia, Xiaona Yang, Xian Zhang","doi":"10.1016/j.physd.2025.134577","DOIUrl":"10.1016/j.physd.2025.134577","url":null,"abstract":"<div><div>In this paper, the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization problem of delayed multi-weight neural networks under switching topologies is investigated. The involved delays include time-varying leakage, transmission and distributed delays. Firstly, a novel controller is designed to ensure <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization between the drive and response multi-weight neural networks. Secondly, a property of solutions of the considered error system is investigated, which forms a basis of obtaining a new criterion of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization. In contrast to the existing ones, the obtained criterion comprises just a small number of simple linear scalar inequalities, thereby amount of computations is greatly reduced. Finally, a numerical example related to communication networks is presented to demonstrate the applicability of the obtained <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization criterion. It is worth noting that the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization control problem of delayed multi-weight neural networks under switching topologies is solved for the first time, and the proposed method is directly based on the definitions of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization, which is easily extended to some switching delayed system models.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134577"},"PeriodicalIF":2.7,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134578

Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi

{"title":"Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs","authors":"Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi","doi":"10.1016/j.physd.2025.134578","DOIUrl":"10.1016/j.physd.2025.134578","url":null,"abstract":"<div><div>Synchronization of populations is a common phenomenon in nature. The high-dimensional Kuramoto model is one of the most typical continuous system models for studying synchronization phenomena in multi-individual systems. Due to Lohe’s remarkable work on models of multi-individual systems, the high-dimensional Kuramoto models are also called the Lohe models, and the Lohe Hermitian sphere (LHS) model is a generalization of the Lohe models in the complex space. In this paper, we study the exponential synchronization problem of the LHS models based on directed graphs. By introducing the synchronization error function, we have developed a set of synchronization error dynamic equations for the identical oscillators using matrix Riccati differential equations. The system of synchronization error dynamic equations is studied, a total error function is constructed, and exponential synchronization of the LHS model on the unit complex sphere is demonstrated. An approximate linearization of the error dynamics equations is performed, to obtain the exponential decay rate of the system. For the LHS model with nonidentical oscillators on the unit complex sphere, using the synchronization error function, it is shown that practical synchronization can be achieved when the connection graph of the system is strongly connected.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134578"},"PeriodicalIF":2.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On periodic solutions for the Maxwell–Bloch equations

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134581

A.I. Komech

引用次数: 0

On the nonexistence of NLS breathers

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-20 DOI: 10.1016/j.physd.2025.134580

Miguel Á. Alejo , Adán J. Corcho

引用次数: 0

Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-19 DOI: 10.1016/j.physd.2025.134579

Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha

{"title":"Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model","authors":"Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha","doi":"10.1016/j.physd.2025.134579","DOIUrl":"10.1016/j.physd.2025.134579","url":null,"abstract":"<div><div>Existence and uniqueness of a stationary-state solution to the nonlinear aggregation and collision-induced fragmentation equation is proved over a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-space. The assumption of a detailed balance condition is relaxed to attain the existence of the solution. Aggregation and fragmentation kernels are considered to exhibit linear and quadratic growth rates respectively which encompass a wide range of physically significant kernels. Asymptotic properties of the time-dependent solution are analyzed in detail and convergence of the same to the stationary-state solution is also examined. Exponential rate of convergence is obtained by proving the asymptotic stability of the stationary-state solution. Further, nonlinear estimates of the solution are obtained using semigroup theory of operators. The study is further extended to analyze the nonexistence of a stationary-state solution for a particular choice of kinetic kernels over a suitably constructed solution space. A numerical example is provided in order to visualize the nonexistence of a stationary-state solution and other physical quantities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134579"},"PeriodicalIF":2.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0