Physica D: Nonlinear Phenomena最新文献

{"title":"Synchronization of branching chain of dynamical systems","authors":"Michele Baia ,&nbsp;Franco Bagnoli ,&nbsp;Tommaso Matteuzzi ,&nbsp;Arkady Pikovsky","doi":"10.1016/j.physd.2025.134664","DOIUrl":"10.1016/j.physd.2025.134664","url":null,"abstract":"<div><div>We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as the parent for the subsequent node. Our analysis focuses on two distinct synchronization behaviors: parent–child synchronization, defined by the vanishing distance between successive nodes along the chain, and sibling synchronization, corresponding to the convergence of the states of two child nodes. Our findings reveal significant differences in these two type of synchronization mechanisms, which are closely associated with the probability distribution of the state of parent node. Theoretical analysis and simulations with the logistic map support our findings. We further investigate numerical aspects of the implementation corresponding to cases for which the simulated regimes differ from the theoretically predicted one due to computational finite accuracy. We perform a detailed study on how instabilities are numerically suppressed or amplified along the chain. In some cases, a properly adjusted computational scheme can solve this problem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134664"},"PeriodicalIF":2.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947153","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":"Exact expression for the propagating front velocity in nonlinear discrete systems under nonreciprocal coupling","authors":"David Pinto-Ramos","doi":"10.1016/j.physd.2025.134665","DOIUrl":"10.1016/j.physd.2025.134665","url":null,"abstract":"<div><div>Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts into the stable state, nonlinear waves appearing in bistable and multistable systems, are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and understanding these waves is then crucial to make use of their properties. Their velocity is one of the most important features, which can be analytically computed only for specific dynamical systems and under restricted conditions on the parameters, and it becomes more elusive in the presence of spatial discreteness and nonreciprocal coupling. A key difficulty in developing expressions for the front velocity is the lack of a front rigid shape exploiting translational invariance, a property that is broken in discrete systems with a finite number of elements. This work reveals that fronts in discrete systems can be treated as rigid objects when analyzing their whole trajectory by collecting the system state at each time step instead of just observing the instantaneous, current state. Then, a relationship between the front velocity and its reconstructed rigid shape is found. Applying this method to a generic model for nonreciprocally coupled bistable systems reveals that the derived velocity formula provides insight into fronts’ long-observed properties, such as the oscillatory trajectory for the front position and the pinning–depinning transition, and agrees with the approximative and parameterized methods described in the literature. Furthermore, it reveals an explicit linear relationship between the velocity and the nonreciprocal coupling constant. Numerical simulations show perfect agreement with the theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134665"},"PeriodicalIF":2.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143835243","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":"Action of viscous stresses on the Young–Laplace equation in Hele-Shaw flows: A gap-averaged calculation","authors":"Eduardo O. Dias,&nbsp;Írio M. Coutinho,&nbsp;José A. Miranda","doi":"10.1016/j.physd.2025.134663","DOIUrl":"10.1016/j.physd.2025.134663","url":null,"abstract":"<div><div>The Saffman–Taylor (or, viscous fingering) instability arises when a less viscous fluid displaces a more viscous one in the narrow gap of a Hele-Shaw cell. The dynamics of the fluid–fluid interface is usually described by a set of gap-averaged equations, including Darcy’s law and fluid incompressibily, supported by the pressure jump (Young–Laplace equation) and kinematic boundary conditions. Over the past two decades, various research groups have studied the influence of viscous normal stresses on the Young–Laplace equation on the development of radial fingering. However, in these works, the contribution of viscous normal stresses is included through the insertion of a legitimately two-dimensional term into the pressure jump condition. As a result, the significant variation of the fluid velocity along the direction perpendicular to the Hele-Shaw plates is neglected. In line with Hele-Shaw flow approximations, and analogous to the derivation of Darcy’s law, we introduce viscous stresses in the Young–Laplace equation through a gap-averaged calculation of the three-dimensional viscous stress tensor. We then compute the contributions of these gap-averaged viscous stresses in both the linear stability and early nonlinear analyses of the interface perturbation evolution. Our findings indicate that this approach leads to a slowdown in finger growth, and an intensification of typical tip-splitting events.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134663"},"PeriodicalIF":2.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839117","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 straightforward construction of Z-graded Lie algebras of full-fledged nonlocal symmetries via recursion operators","authors":"Jiřina Jahnová,&nbsp;Petr Vojčák","doi":"10.1016/j.physd.2025.134658","DOIUrl":"10.1016/j.physd.2025.134658","url":null,"abstract":"<div><div>We consider the reduced quasi-classical self-dual Yang–Mills equation (rYME) and two recently found (Jahnová and Vojčák, 2024) invertible recursion operators <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> for its full-fledged (in a given differential covering) nonlocal symmetries. We introduce a <span><math><mi>Z</mi></math></span>-grading on the Lie algebra <span><math><mrow><msubsup><mrow><mi>sym</mi></mrow><mrow><mi>L</mi></mrow><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mi>W</mi></mrow></msup></mrow></msubsup><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> of all nonlocal Laurent polynomial symmetries of the rYME and prove that both the operators <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> are <span><math><mi>Z</mi></math></span>-graded automorphisms of the underlying vector space on the set <span><math><mrow><msubsup><mrow><mi>sym</mi></mrow><mrow><mi>L</mi></mrow><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mi>W</mi></mrow></msup></mrow></msubsup><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span>. This <em>inter alia</em> implies that all its vector subspaces formed by all homogeneous elements of a given fixed degree (i.e. a weight in the context below) are mutually isomorphic, and thus each of them can be uniquely reconstructed from the vector space of all homogeneous symmetries of the zero degree. To the best of our knowledge, such a result is unparalleled in the current body of literature. The obtained results are used for the construction of a Lie subalgebra <span><math><mi>V</mi></math></span> of <span><math><mrow><msubsup><mrow><mi>sym</mi></mrow><mrow><mi>L</mi></mrow><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mi>W</mi></mrow></msup></mrow></msubsup><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> which contains all known to us nonlocal Laurent polynomial symmetries of the rYME. The Lie algebra <span><math><mi>V</mi></math></span> is subsequently described as the linear span of the orbits of a set of selected zero-weight symmetries — we refer to them as to the seed generators of <span><math><mi>V</mi></math></span>. Further, we study the hierarchies of symmetries related to the seed generators under the action of the group of recursion operators generated by <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>. Finally, the linear dependence/independence of the (sub)set of generators of <span><math><mi>V</mi></math></span> is discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134658"},"PeriodicalIF":2.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143843967","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":"Neural network solutions to the critical SQG equations via approximating nonlocal periodic operators","authors":"Elie Abdo ,&nbsp;Ruimeng Hu ,&nbsp;Quyuan Lin","doi":"10.1016/j.physd.2025.134652","DOIUrl":"10.1016/j.physd.2025.134652","url":null,"abstract":"<div><div>Nonlocal periodic operators in partial differential equations (PDEs) pose challenges in constructing neural network solutions, which typically lack periodic boundary conditions. In this paper, we introduce a novel PDE perspective on approximating these nonlocal periodic operators. Specifically, we investigate the behavior of the periodic first-order fractional Laplacian and Riesz transform when acting on nonperiodic functions, thereby initiating a new PDE theory for approximating solutions to equations with nonlocalities using neural networks. Moreover, we derive quantitative Sobolev estimates and utilize them to rigorously construct neural networks that approximate solutions to the two-dimensional periodic critically dissipative Surface Quasi-Geostrophic (SQG) equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134652"},"PeriodicalIF":2.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824171","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":"Bridging Algorithmic Information Theory and Machine Learning: Clustering, density estimation, Kolmogorov complexity-based kernels, and kernel learning in unsupervised learning","authors":"Boumediene Hamzi ,&nbsp;Marcus Hutter ,&nbsp;Houman Owhadi","doi":"10.1016/j.physd.2025.134669","DOIUrl":"10.1016/j.physd.2025.134669","url":null,"abstract":"<div><div>Machine Learning (ML) and Algorithmic Information Theory (AIT) offer distinct yet complementary approaches to understanding and addressing complexity. This paper investigates the synergy between these disciplines in two directions: <em>AIT for Kernel Methods</em> and <em>Kernel Methods for AIT</em>. In the former, we explore how AIT concepts inspire the design of kernels that integrate principles like relative Kolmogorov complexity and normalized compression distance (NCD). We propose a novel clustering method utilizing the Minimum Description Length principle, implemented via K-means and Kernel Mean Embedding (KME). Additionally, we apply the Loss Rank Principle (LoRP) to learn optimal kernel parameters in the context of Kernel Density Estimation (KDE), thereby extending the applicability of AIT-inspired techniques to flexible, nonparametric models. In the latter, we show how kernel methods can be used to approximate measures such as NCD and Algorithmic Mutual Information (AMI), providing new tools for compression-based analysis. Furthermore, we demonstrate that the Hilbert–Schmidt Independence Criterion (HSIC) approximates AMI, offering a robust theoretical foundation for clustering and other dependence-measurement tasks. Building on our previous work introducing Sparse Kernel Flows from an AIT perspective, we extend these ideas to unsupervised learning, enhancing the theoretical robustness and interpretability of ML algorithms. Our results demonstrate that kernel methods are not only versatile tools for ML but also crucial for bridging AIT and ML, enabling more principled approaches to unsupervised learning tasks.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134669"},"PeriodicalIF":2.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821114","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":"Analytic soliton solutions of nonlinear extensions of the Schrödinger equation","authors":"Tom Dodge ,&nbsp;Peter Schweitzer","doi":"10.1016/j.physd.2025.134666","DOIUrl":"10.1016/j.physd.2025.134666","url":null,"abstract":"<div><div>A method is presented to construct analytic solitary wave solutions in nonlinear extensions of the Schrödinger equation starting from analytic solutions of the ordinary Schrödinger equation. We provide several examples illustrating the method. We rederive three well-known soliton solutions including the <span><math><mi>N</mi></math></span>-dimensional non-relativistic Gausson as well as the one-dimensional <span><math><mrow><mn>1</mn><mo>/</mo><mo>cosh</mo></mrow></math></span>-soliton and a theory with a power-like nonlinearity proportional to <span><math><msup><mrow><mrow><mo>|</mo><mi>Ψ</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn><mi>λ</mi></mrow></msup></math></span> with <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We also find several new solutions in different nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134666"},"PeriodicalIF":2.7,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143830078","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":"Hopf–Hopf bifurcation of the memory-based diffusive bacterial infection model","authors":"Ali Rehman,&nbsp;Ranchao Wu","doi":"10.1016/j.physd.2025.134653","DOIUrl":"10.1016/j.physd.2025.134653","url":null,"abstract":"<div><div>Bacterial infections challenge the immune system, causing inflammation in which leukocytes play an important role in identifying and combating harmful bacteria. These white blood cells, leukocytes, navigate to infection sites by chemotaxis, which is guided by chemical cues from bacteria. The leukocytes then either engulf and destroy the harmful bacteria or release enzymes to neutralize the infection. This phenomenon is crucial for controlling infections and preventing their spread. However, this process is influenced by memory effects, which cause their movement to be affected by previous signals, as well as reaction delays. These variables complicate immune responses, thus understanding their impact on infection dynamics and inflammation is critical for developing better treatments. In this paper, we analyze a diffusive bacterial infection model with a spatial memory effect, taking into account the impact of delay on the movement of leukocytes. Through stability and bifurcation analysis, we obtain the sufficient and necessary conditions for the Hopf bifurcation and stability switches. It is found that in the absence of delay the system remains stable under certain conditions. However, in the presence of time delay, the system will undergo the Hopf bifurcation, when the time delay exceeds a critical threshold, and the stability of the equilibrium point is affected by the memory delay, leading to inhomogeneous spatially periodic oscillations. Moreover, we explore the occurrence of Hopf–Hopf bifurcation and the stability switches. The induced Hopf–Hopf bifurcation is further studied in detail based on normal form theory and the center manifold theorem. Finally, numerical simulations are provided to validate our theoretical findings.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134653"},"PeriodicalIF":2.7,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799803","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":"Weighted Visibility Graph-based Deep Complex Network Features: New Diagnostic Spontaneous Speech Markers of Alzheimer's Disease","authors":"Mahda Nasrolahzadeh ,&nbsp;Zeynab Mohammadpoory ,&nbsp;Javad Haddadnia","doi":"10.1016/j.physd.2025.134681","DOIUrl":"10.1016/j.physd.2025.134681","url":null,"abstract":"<div><div>Recognition of dynamic complexity changes in spontaneous speech signals can be regarded as a significant criterion for the early diagnosis of Alzheimer's disease (AD). Using the information embedded in spontaneous speech signals, in the framework of computational geometry; this paper introduces a new method for classifying speech diversity differences of healthy subjects compared to those with three stages of AD. Due to the dynamic and nonlinear nature of the speech signals, a weighted visibility graph (WVG) is proposed as a quantitative approach based on the concept of strength between nodes. The differential complexities of the network among the people of the four groups are analyzed using two criteria: average weighted degree and modularity. A long short-term memory (LSTM) network-based deep architecture is used to classify AD stages allied to its performance dealing with WVG-based features. The results show that the proposed algorithm has outstanding accuracy compared to its rivals in detecting the early stages of AD. It can classify speech signals into four groups with a high accuracy of 99.75%. In addition, the proposed approach has the potential to make it much easier to adopt the running state of the speech generation system and the central nervous system disorders affecting language skills by revealing significant differences between the speech reactions of the four mentioned groups. Therefore, it can be a valuable tool for evaluating AD in its preclinical stages.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134681"},"PeriodicalIF":2.7,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821115","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":"Improved buoyancy-drag model based on mean density profile and mass conservation principle","authors":"Qi-xiang Li (李玘祥) ,&nbsp;You-sheng Zhang (张又升)","doi":"10.1016/j.physd.2025.134673","DOIUrl":"10.1016/j.physd.2025.134673","url":null,"abstract":"<div><div>Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) turbulent mixing occur frequently in various natural phenomena and practical engineering applications. Accurate prediction of the evolution of mixing width, which comprises the bubble mixing width (BMW) and spike mixing width (SMW), holds significant scientific and engineering importance. Over the past several decades, buoyancy-drag models have been widely used to predict this evolution, but these models exhibit several limitations. In this paper, we propose a new buoyancy-drag model that incorporates additional physical constraints. The new model posits that the evolutions of the BMW and SMW are interrelated and mutually dependent. Consequently, we innovatively introduce the principle of mass conservation to link the evolution of SMW to that of BMW. The BMW is modeled using an ordinary differential equation (ODE) that includes inertial force, drag, and buoyancy terms. Accurate modeling of the inertial force term requires knowledge of the mean density profile, which we analytically derived for any density ratio by improving the previous density-ratio-invariant mean-species profile theory. The form and coefficient of the drag term were determined inversely by imposing the constraint that the ODE must predict the physical evolution of RM mixing. For the buoyancy term, we accounted for the entrainment phenomenon by introducing a density-ratio-dependent buoyancy coefficient additionally. The specific form of this coefficient was derived by requiring that the ODE predict the physical evolution of RT mixing as the density ratio approaches 1. Using a single set of coefficients, the new model successfully predicted the physical evolution of the mixing width across different density ratios and acceleration histories. This study enhances both the accuracy and robustness of the buoyancy-drag model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134673"},"PeriodicalIF":2.7,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815969","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}