Physica D: Nonlinear Phenomena最新文献

{"title":"An experimental observation of intermittent extreme events in boundary layer transition","authors":"G. Balamurugan ,&nbsp;S.S. Gopalakrishnan ,&nbsp;A.C. Mandal","doi":"10.1016/j.physd.2025.134598","DOIUrl":"10.1016/j.physd.2025.134598","url":null,"abstract":"<div><div>One of the fundamental characteristics of an extreme event, which has been widely studied in diverse branches of physics, is the non-Gaussian nature of the probability distribution function. Specifically events which have amplitudes that are twice the significant wave height, which is a measure of the background state, are characterized as extreme events. Here we find a parallel of this event during the laminar–turbulent transition in a flat-plate boundary layer subjected to freestream turbulence. During the transition process spontaneous intermittent turbulent fluctuations are observed with amplitudes twice the significant wave height of the background state. The probability distribution function of events during the transition process is quantified using hotwire anemometry revealing a long-tail non-Gaussian nature as a whole, which is a fundamental characteristic of extreme events. The spatial structure of extreme fluctuation shows that they are large amplitude spatially localized structures which were obtained from simultaneous measurements made using hot-wire and time-resolved particle image velocimetry techniques. The probability of occurrence of such high intensity spatially localized turbulent fluctuations increases with the freestream velocity. Though the phenomenon of intermittency during boundary layer transition has been extensively studied, the objective of the present work is to establish its similarities to extreme events predicted in other fields of physics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134598"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592756","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}

{"title":"Periodic orbits and integrability of Rocard’s system","authors":"Xinhao Hu,&nbsp;Yilei Tang","doi":"10.1016/j.physd.2025.134594","DOIUrl":"10.1016/j.physd.2025.134594","url":null,"abstract":"<div><div>In 1941, based on Van der Pol’s relaxation oscillator equation, physicist Yves Rocard in the book (Rocard 1941) proposed a relaxation econometric oscillator to describe cyclical oscillations in the economy. Furthermore, it was later found that the model exhibits chaotic phenomenon. Rocard’s chaotic system predates Lorenz’s discovery by 22 years, which is a three-dimensional autonomous differential system. In this paper, we research periodic orbits and integrability of Rocard’s system. We study the zero-Hopf bifurcation near equilibria and center problem on center manifolds, proving that one or three periodic orbits can bifurcate through the application of the averaging method up to arbitrary finite order, while obtaining center conditions for all equilibria through Lyapunov method. Furthermore, we investigate the integrability of Rocard’s system, which has no algebraic first integrals, Darboux polynomials, or Darboux first integrals, and is not Liouvillian integrable.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134594"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549612","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}

{"title":"How to quantify interaction strengths? A critical rethinking of the interaction Jacobian and evaluation methods for non-parametric inference in time series analysis","authors":"Takeshi Miki ,&nbsp;Chun-Wei Chang ,&nbsp;Po-Ju Ke ,&nbsp;Arndt Telschow ,&nbsp;Cheng-Han Tsai ,&nbsp;Masayuki Ushio ,&nbsp;Chih-hao Hsieh","doi":"10.1016/j.physd.2025.134613","DOIUrl":"10.1016/j.physd.2025.134613","url":null,"abstract":"<div><div>Quantifying interaction strengths between state variables in dynamical systems is essential for understanding ecological networks. Within the empirical dynamic modeling approach, multivariate S-map infers the interaction Jacobian from multivariate time series data without assuming specific dynamical models. This approach enables the non-parametric statistical inference of interspecific interactions through state space reconstruction. However, deviations in the biological interpretation and numerical implementation of the interaction Jacobian from its unique mathematical definition pose challenges. We mathematically reintroduce the interaction Jacobian by starting our derivation with differential quotients, uncovering two key problems: (1) the mismatch between the interaction Jacobian and its biological meaning complicates comparisons between interspecific and intraspecific interaction strengths; (2) the interaction Jacobian is not fully implemented in the parametric Jacobian numerically derived from given parametric models, especially ordinary differential equation models. As a result, model-based evaluations of S-map methods become inappropriate. To address these problems, (1) we propose adjusting the diagonal elements of the interaction Jacobian by subtracting 1 to resolve the comparability problem between interspecific and intraspecific interaction strengths. Simulations of population dynamics showed that this adjustment prevents overestimation of intraspecific interaction strengths, allowing for meaningful comparisons. (2) We introduce an alternative parametric Jacobian and then cumulative interaction strength (CIS), providing a more rigorous benchmark for evaluating S-map methods. Furthermore, we demonstrated that the numerical gap between CIS and the existing parametric Jacobian is substantial in realistic scenarios, suggesting CIS as a preferred benchmark for future evaluations. These solutions offer a clearer framework for developing non-parametric approaches in ecological time series analysis.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134613"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629411","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}

{"title":"Light-induced matter vortex transitions","authors":"P.J. Aguilera-Rojas,&nbsp;M.G. Clerc,&nbsp;M. Diaz-Zuniga,&nbsp;R. Gajardo-Pizarro","doi":"10.1016/j.physd.2025.134599","DOIUrl":"10.1016/j.physd.2025.134599","url":null,"abstract":"<div><div>Optical vortices have attracted attention due to their intrinsic characteristics and potential applications, which span from telecommunication in free space and image analysis to manipulating small particles. Optical valves and liquid crystal cells have been fundamental in generating optical vortex beams. The theoretical description predicts the existence of different Rayleigh and standard vortices. Based on two different experiments, we investigate the transition between these vortices. When the effect of topological forcing is dominant, the bifurcation diagram between these vortices has been characterized through both experimental and numerical means. The numerical and experimental findings present qualitative agreement.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134599"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579634","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}

{"title":"Automatic classification of magnetic field line topology by persistent homology","authors":"N. Bohlsen ,&nbsp;V. Robins ,&nbsp;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}

{"title":"Giant vortex in a harmonically-trapped rotating dipolar 164Dy condensate","authors":"Luis E. Young-S. ,&nbsp;S.K. Adhikari","doi":"10.1016/j.physd.2025.134590","DOIUrl":"10.1016/j.physd.2025.134590","url":null,"abstract":"<div><div>We demonstrate the formation of dynamically stable giant vortices in a harmonically-trapped strongly dipolar ¹⁶⁴Dy Bose–Einstein condensate under rotation around the polarization direction of dipolar atoms, employing the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction, meant to stop a collapse at high atom density. These giant vortices are stationary, obtainable by imaginary-time propagation using a Gaussian initial state, while the appropriate phase of the giant vortex is imprinted on the initial wave function. The dynamical stability of the giant vortices is established by real-time propagation during a long interval of time after a small change of a parameter.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134590"},"PeriodicalIF":2.7,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549613","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}

{"title":"Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition","authors":"Zhi-Xuan Meng ,&nbsp;Shuai-Xia Xu ,&nbsp;Yu-Qiu Zhao","doi":"10.1016/j.physd.2025.134589","DOIUrl":"10.1016/j.physd.2025.134589","url":null,"abstract":"<div><div>In the present paper, we study the time-dependent correlation function of the one-dimensional impenetrable Bose gas, which can be expressed in terms of the Fredholm determinant of a time-dependent sine kernel and the solutions of the separated NLS equations. We derive the large time and distance asymptotic expansions of this determinant and the solutions of the separated NLS equations in both the space-like region and time-like region of the <span><math><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></math></span>-plane. Furthermore, we observe a phase transition between the asymptotic expansions in these two different regions. The phase transition is then shown to be described by a particular solution of the Painlevé IV equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134589"},"PeriodicalIF":2.7,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526610","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}

{"title":"Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems","authors":"Shane A. McQuarrie ,&nbsp;Anirban Chaudhuri ,&nbsp;Karen E. Willcox ,&nbsp;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}

{"title":"Lp stability-based synchronization of delayed multi-weight neural networks under switching topologies","authors":"Yunxiao Jia,&nbsp;Xiaona Yang,&nbsp;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}

{"title":"Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs","authors":"Xinyun Liu ,&nbsp;Wei Li ,&nbsp;Xueyan Li ,&nbsp;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}