Physica D: Nonlinear Phenomena最新文献

{"title":"A statistical complexity measure can differentiate Go/NoGo trials during a visual-motor task using human electroencephalogram data","authors":"Francisco Leandro P. Carlos ,&nbsp;Maria Carla Navas ,&nbsp;Ícaro Rodolfo Soares Coelho Da Paz ,&nbsp;Helena Bordini de Lucas ,&nbsp;Maciel-Monteiro Ubirakitan ,&nbsp;Marcelo Cairrão Araújo Rodrigues ,&nbsp;Moises Aguilar Domingo ,&nbsp;Eva Herrera-Gutiérrez ,&nbsp;Osvaldo A. Rosso ,&nbsp;Luz Bavassi ,&nbsp;Fernanda Selingardi Matias","doi":"10.1016/j.physd.2025.134955","DOIUrl":"10.1016/j.physd.2025.134955","url":null,"abstract":"<div><div>Complexity is a ubiquitous concept in contemporary science and everyday life. A complex dynamical system is usually characterized by a blend of order and disorder, as well as emergent phenomena that often span multiple temporal and spatial scales. The information processes related to different cognitive processes in the brain can be studied in light of statistical differences based on complexity measures of the electrophysiological time series from different trial types. Recently, it has been demonstrated that a symbolic information approach can be a valuable tool for discriminating response-related differences between Go and NoGo trials using the local field potential of brain regions in monkeys. The method shows significant differences between trial types earlier than the simple average of the electrical signals. Here, we analyze human electroencephalogram data during a Go/NoGo task using information-theoretical quantifiers, including entropy and complexity. We employ the Bandt–Pompe symbolization methodology to determine a probability distribution function for each time series and then to calculate information theory indices. We show that a few channels, especially a central and an occipital electrode, consistently differentiate Go/NoGo trials at the individual level. We also show that different trial types occupy separate regions in the complexity-entropy plane. Our method also captures specific time windows to better differentiate the trial type. Moreover, we show that our results are robust at the group level, considering the average activity of all subjects.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134955"},"PeriodicalIF":2.9,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267937","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":"An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler–Coulomb models","authors":"Francisco J. Herranz ,&nbsp;Danilo Latini","doi":"10.1016/j.physd.2025.134963","DOIUrl":"10.1016/j.physd.2025.134963","url":null,"abstract":"<div><div>This work aims to bridge the gap between Dunkl superintegrable systems and the coalgebra symmetry approach to superintegrability, and subsequently to recover known models and construct new ones. In particular, an infinite family of <span><math><mi>N</mi></math></span>-dimensional quasi-maximally superintegrable quantum systems with reflections, sharing the same set of <span><math><mrow><mn>2</mn><mi>N</mi><mo>−</mo><mn>3</mn></mrow></math></span> quantum integrals, is introduced. The result is achieved by introducing a novel differential–difference realization of <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> and then applying the coalgebra formalism. Several well-known maximally superintegrable models with reflections appear as particular cases of this general family, among them, the celebrated Dunkl oscillator and the Dunkl–Kepler–Coulomb system. Furthermore, restricting to the case of “hidden” quantum quadratic symmetries, maximally superintegrable curved oscillator and Kepler–Coulomb Hamiltonians of Dunkl type, sharing the same underlying <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> coalgebra symmetry, are presented. Namely, the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on the <span><math><mi>N</mi></math></span>-sphere and hyperbolic space together with two models which can be interpreted as a one-parameter superintegrable deformation of the Dunkl oscillator and the Dunkl–Kepler–Coulomb system on non-constant curvature spaces. In addition, maximally superintegrable generalizations of these models, involving non-central potentials, are also derived on flat and curved spaces. For all specific systems, at least an additional quantum integral is explicitly provided, which is related to the Dunkl version of a (curved) Demkov–Fradkin tensor or a Laplace–Runge–Lenz vector.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134963"},"PeriodicalIF":2.9,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267934","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":"Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model","authors":"D.S. Agafontsev ,&nbsp;T. Congy ,&nbsp;G.A. El ,&nbsp;S. Randoux ,&nbsp;G. Roberti ,&nbsp;P. Suret","doi":"10.1016/j.physd.2025.134956","DOIUrl":"10.1016/j.physd.2025.134956","url":null,"abstract":"<div><div>We use the spectral theory of soliton gas for the one-dimensional focusing nonlinear Schrödinger equation (fNLSE) to describe the statistically stationary and spatially homogeneous integrable turbulence emerging at large times from the evolution of the spontaneous (noise-induced) modulational instability of the elliptic “dn” fNLSE solutions. We show that a special, critically dense, soliton gas, namely the genus one bound-state soliton condensate, represents an accurate model of the asymptotic state of the “elliptic” integrable turbulence. This is done by first analytically evaluating the relevant spectral density of states which is then used for implementing the soliton condensate numerically via a random <span><math><mi>N</mi></math></span>-soliton ensemble with <span><math><mi>N</mi></math></span> large. A comparison of the statistical parameters, such as the Fourier spectrum, the probability density function of the wave intensity, and the autocorrelation function of the intensity, of the soliton condensate with the results of direct numerical fNLSE simulations with <span><math><mi>dn</mi></math></span> initial data augmented by a small statistically uniform random perturbation (a noise) shows a remarkable agreement. Additionally, we analytically compute the kurtosis of the elliptic integrable turbulence, which enables one to estimate the deviation from Gaussianity. The analytical predictions of the kurtosis values, including the frequency of its temporal oscillations at the intermediate stage of the modulational instability development, are also shown to be in excellent agreement with numerical simulations for the entire range of the elliptic parameter <span><math><mi>m</mi></math></span> of the initial <span><math><mi>dn</mi></math></span> potential.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134956"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221171","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":"On blowup solution in NLS equation under dispersion or nonlinearity management","authors":"Jing Li ,&nbsp;Ying He ,&nbsp;Cui Ning ,&nbsp;Xiaofei Zhao","doi":"10.1016/j.physd.2025.134957","DOIUrl":"10.1016/j.physd.2025.134957","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study the dispersion-managed nonlinear Schrödinger (DM-NLS) equation &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and the nonlinearity-managed NLS (NM-NLS) equation: &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a periodic function which is equal to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and is equal to 1 when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The two models share the feature that the focusing and defocusing effects convert periodically. For the classical focusing NLS, it is known that the initial data &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mr","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134957"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221165","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":"Essential metrics for Life on graphs","authors":"Michiel Rollier ,&nbsp;Lucas Caldeira de Oliveira ,&nbsp;Odemir M. Bruno ,&nbsp;Jan M. Baetens","doi":"10.1016/j.physd.2025.134950","DOIUrl":"10.1016/j.physd.2025.134950","url":null,"abstract":"<div><div>We present a strong theoretical foundation that frames a well-defined family of outer-totalistic network automaton models as a topological generalisation of binary outer-totalistic cellular automata, of which the Game of Life is one notable particular case. These “Life-like network automata” are quantitatively described by expressing their genotype (the mean field curve and Derrida curve) and phenotype (the evolution of the state and defect averages). After demonstrating that the genotype and phenotype are correlated, we illustrate the utility of these essential metrics by tackling the firing squad synchronisation problem in a bottom-up fashion, with results that exceed a 90% success rate.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134950"},"PeriodicalIF":2.9,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267933","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":"RTC-fPINNs: Respecting temporal causality fPINNs method for time fractional fourth order partial differential equations","authors":"Zhenqi Qi ,&nbsp;Jieyu Shi ,&nbsp;Xiaozhong Yang","doi":"10.1016/j.physd.2025.134962","DOIUrl":"10.1016/j.physd.2025.134962","url":null,"abstract":"<div><div>The accuracy of conventional fractional physics-informed neural networks (fPINNs) approach suffers dramatically for time fractional partial differential equations (PDEs) with high order derivative and strong nonlinearity. In this paper, a new respecting temporal causality fPINNs (RTC-fPINNs) method for solving time fractional fourth order PDEs is studied. To start with, an auxiliary function is introduced to transform the objective equations into two second order physical systems. Next, the Caputo fractional derivative is approximated through the L1 scheme on graded mesh for resolving the solution’s initial singularity, and correspondingly, the integer order derivatives are obtained via leveraging automatic differentiation of neural networks. Then, the reformulation loss functions corresponding to soft and hard constraints of boundary conditions are adopted to respect the intrinsic causal structure of the physical systems when training the neural network models. Finally, various numerical scenarios, including time fractional fourth order subdiffusion equation, time fractional Kuramoto–Sivashinsky and Cahn–Hilliard equations, are conducted to validate the remarkable effectiveness and robustness of the RTC-fPINNs method. It is noteworthy that, when using the same parameter values, the error accuracy of the established RTC-fPINNs approach is significantly better than that of the conventional fPINNs method.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134962"},"PeriodicalIF":2.9,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221166","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":"Anti-aligning interaction induces gyratory flocking of simple self-propelled particles: The impact of translational noise","authors":"Daniel Escaff","doi":"10.1016/j.physd.2025.134960","DOIUrl":"10.1016/j.physd.2025.134960","url":null,"abstract":"<div><div>This report considers a set of simple active particles (non-self-rotating particles) interacting due to a purely anti-aligning force. Recently, it has been shown that such anti-aligning interaction may induce a finite wavelength instability. The instability occurs with an oscillatory frequency. Consequently, the system displays pattern formation. The formed patterns consist of propagative dissipative structures (two counterpropagating traveling waves). Here, we explore the impact of including translational noise in the dynamics. The finite wavelength instability persists; however, the oscillatory frequency only persists if the particle’s self-propulsion speed is larger enough than the translational noise intensity. We focus on this case. Near criticality, where fluctuations predominate, it is possible to distinguish propagative patterns. Moving away from criticality, a new pattern emerges via a secondary transition. Namely, a hexagonal structure formed of rotating clusters. These clusters rotate in unison, giving rise to a global gyratory synchrony. This secondary transition is discontinuous. Finally, we discuss the main ingredients that induce this sort of rotatory synchronization, showing that short-range repulsion might produce a similar effect to translational noise.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134960"},"PeriodicalIF":2.9,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221168","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":"On the long-time asymptotics of the complex mKdV equation with step-like oscillating background","authors":"Qingshan Tan,&nbsp;Weifang Weng,&nbsp;Jian Zhang","doi":"10.1016/j.physd.2025.134945","DOIUrl":"10.1016/j.physd.2025.134945","url":null,"abstract":"<div><div>In this paper, we investigate the Cauchy problem for the complex mKdV equation with initial data approaching two different plane waves of the form <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>j</mi></mrow></msub><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mn>2</mn><mi>i</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>j</mi></mrow></msub><mi>x</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span> as <span><math><mrow><mi>x</mi><mo>→</mo><mo>±</mo><mi>∞</mi></mrow></math></span>. By performing the nonlinear steepest descent analysis and the so-called g-function mechanism, we deform the original oscillatory matrix Riemann-Hilbert problem into explicitly solvable model problems and show that the solution of step-like initial value problem exhibits rich long-time asymptotics. We mainly consider some possible sectors of the <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo></mrow></math></span>plane under a specific choice of parameter and derive exact asymptotic formulas for the solution. Furthermore, we rigorously establish the existence of the g-functions for certain asymptotic sectors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134945"},"PeriodicalIF":2.9,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267935","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":"A novel three-dimensional chaotic system with spiral chaos and adjustable number of wings: application in weak underwater acoustic signal detection","authors":"Hong Yang,&nbsp;Shijia Wang,&nbsp;Guohui Li","doi":"10.1016/j.physd.2025.134965","DOIUrl":"10.1016/j.physd.2025.134965","url":null,"abstract":"<div><div>To address the shortcomings of traditional two-dimensional chaotic systems in detection performance, this paper proposes a novel three-dimensional (3D) four-wing chaotic system (3DFWCS) with spiral chaos and adjustable number of wings, and applies it to weak underwater acoustic signal detection. First, the nonlinear characteristics of 3DFWCS, such as bifurcation and Lyapunov exponent, are analyzed in detail. Second, an innovative threshold determination method based on Poincaré section mapping and fractional order refined composite multiscale fluctuation dispersion entropy is proposed. The change in the number of wings in the phase trajectory from two wings to four wings is used as the critical state for weak signal detection. Performance testing demonstrates a detection signal-to-noise ratio lower limit of -107.44 dB. Next, transient transition phenomena of the system are analyzed, revealing that the formation of four wings depends on the negative half-axis of the timing diagram of the state variable <em>z</em>. Finally, a weak signal detection method based on 3DFWCS is proposed and successfully applied to the detection of multi-spectrum periodic signals, distorted signal, ship radiated noise, and marine biological signal, verifying the effectiveness and engineering feasibility of the proposed detection method.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134965"},"PeriodicalIF":2.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267936","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":"Hamiltonian Monte Carlo with asymmetrical momentum distributions","authors":"Soumyadip Ghosh,&nbsp;Yingdong Lu,&nbsp;Tomasz Nowicki","doi":"10.1016/j.physd.2025.134952","DOIUrl":"10.1016/j.physd.2025.134952","url":null,"abstract":"<div><div>Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new dynamical and probabilistic arguments. The convergence is rigorously established under significantly weaker conditions, which among others allow for general auxiliary distributions. In our framework, we show that plain HMC with asymmetrical momentum distributions breaks a key self-adjointness requirement. We propose a modified version of HMC, that we call the Alternating Direction HMC (AD-HMC), which overcomes this difficulty. Sufficient conditions are established under which AD-HMC exhibits geometric convergence in Wasserstein distance. The geometric convergence analysis is extended to when the Hamiltonian motion is approximated by the leapfrog symplectic integrator, where an additional Metropolis–Hastings rejection step is required. Numerical experiments suggest that AD-HMC can generalize a popular dynamic auxiliary scheme to show improved performance over HMC with Gaussian auxiliaries.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134952"},"PeriodicalIF":2.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221170","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}