Physica D: Nonlinear Phenomena最新文献

{"title":"Synchrony and canards in two coupled FitzHugh–Nagumo equations","authors":"Bruno F.F. Gonçalves ,&nbsp;Isabel S. Labouriau ,&nbsp;Alexandre A.P. Rodrigues","doi":"10.1016/j.physd.2025.134853","DOIUrl":"10.1016/j.physd.2025.134853","url":null,"abstract":"<div><div>We describe the fast–slow dynamics of two FitzHugh–Nagumo equations coupled symmetrically through the slow equations. We use symmetry arguments to find a non-empty open set of parameter values for which the two equations synchronise, and another set with antisynchrony – where the solution of one equation is minus the solution of the other. By combining the dynamics within the synchrony and antisynchrony subspaces, we also obtain bistability – where these two types of solution coexist as hyperbolic attractors. They persist under small perturbation of the parameters. Canards are shown to give rise to mixed-mode oscillations. They also initiate small amplitude transient oscillations before the onset of large amplitude relaxation oscillations. We also discuss briefly the effect of asymmetric coupling, with periodic forcing of one of the equations by the other. We illustrate our results with numerical simulations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134853"},"PeriodicalIF":2.9,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988793","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 frequency-domain differential corrector for quasi-periodic trajectory design and analysis","authors":"Beom Park ,&nbsp;Kathleen C. Howell ,&nbsp;Shaun Stewart","doi":"10.1016/j.physd.2025.134882","DOIUrl":"10.1016/j.physd.2025.134882","url":null,"abstract":"<div><div>This paper introduces the Frequency-Domain Differential Corrector (FDDC), a model-agnostic approach for constructing quasi-periodic orbits (QPOs) across a range of dynamical regimes. In contrast to existing methods that explicitly enforce an invariance condition in all frequency dimensions, the FDDC targets dominant spectral components identified through frequency-domain analysis. Leveraging frequency refinement strategies such as Laskar-Numerical Analysis of Fundamental Frequency (L-NAFF) and Gómez-Mondelo-Simó-Collocation (GMS-C), the method enables efficient and scalable generation of high-dimensional QPOs. The FDDC is demonstrated in both single- and multiple-shooting formulations. While the study focuses on the Earth–Moon system, the framework is broadly applicable to other celestial environments. Sample applications include Distant Retrograde Orbits (DROs), Elliptical Lunar Frozen Orbits (ELFOs), and Near Rectilinear Halo Orbits (NRHOs), illustrating constellation design and the recovery of analog solutions in higher-fidelity models. With its model-independent formulation and spectral targeting capabilities, FDDC offers a versatile tool for robust trajectory design and mission planning in complex dynamical systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134882"},"PeriodicalIF":2.9,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932775","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":"Dynamics of localised states in the stochastic discrete nonlinear Schrödinger equation","authors":"Mahdieh Ebrahimi ,&nbsp;Barbara Drossel ,&nbsp;Wolfram Just","doi":"10.1016/j.physd.2025.134905","DOIUrl":"10.1016/j.physd.2025.134905","url":null,"abstract":"<div><div>We revisit aspects of dynamics and stability of localised states in the deterministic and stochastic discrete nonlinear Schrödinger equation. By a combination of analytic and numerical techniques, we show that for deterministic motion localised initial conditions disperse if the strength of the nonlinear part drops below a threshold and that localised states are unstable in a noisy environment. As expected, the constants of motion in the nonlinear Schrödinger equation play a crucial role. An infinite temperature state emerges when multiplicative noise is applied, while additive noise yields unbounded dynamics since conservation of normalisation is violated.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134905"},"PeriodicalIF":2.9,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922539","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":"Flow structures beneath stationary waves with constant vorticity over variable topography","authors":"L.G. Martins ,&nbsp;M.V. Flamarion ,&nbsp;R. Ribeiro -Jr","doi":"10.1016/j.physd.2025.134824","DOIUrl":"10.1016/j.physd.2025.134824","url":null,"abstract":"<div><div>The flow structures beneath waves have received significant attention from both theoretical and numerical perspectives. Most studies on this topic assume a flat bottom, leading to questions about the effects of variable bottom topography. To address this gap, we investigate the flow structures beneath stationary waves with constant vorticity, considering the influence of variable topography. Specifically, we numerically analyze the role of vorticity in the emergence of stagnation points and the pressure distribution within the fluid in two bottom topography scenarios: a bump and a hole. Our numerical approach is based on a variation of the classical Dyachenko, Zakharov, and Kuznetsov conformal mapping technique for free-boundary water wave problems. Our results reveal the existence of saddle points beneath wave crests and center beneath depression solitary waves. Additionally, we observe that the pressure can exhibit distinctive features, such as a global minimum on the bottom boundary – behavior that is markedly different from the usual flat-bottom case.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134824"},"PeriodicalIF":2.9,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922542","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":"Kats–Kontorovich anisotropic solution in simulations of ocean swell","authors":"Sergei I. Badulin ,&nbsp;Vladimir V. Geogjaev ,&nbsp;Andrei N. Pushkarev","doi":"10.1016/j.physd.2025.134906","DOIUrl":"10.1016/j.physd.2025.134906","url":null,"abstract":"<div><div>The physical setup of ocean swell is used as a testbed for the results of the weak turbulence theory. The numerical study with the novel Geogjaev-Zakharov approach highlights the importance of isotropic direct and inverse cascade solutions, along with the self-similarity concept of wave spectra, as developed by Vladimir Zakharov and his collaborators. The approximate anisotropic solution proposed by Kats and Kontorovich in 1970-ies is shown to fit wave spectra well at frequencies exceeding three times the spectral peak frequency. This solution can be interpreted as an attractor for a wide variety of initial distributions of a random wave field. In this context, it is a counterpart to the classic isotropic Kolmogorov-Zakharov solutions. The corresponding Kolmogorov constant of the wave momentum transfer is derived analytically. The study also discusses the implications of these results for sea wave modeling.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134906"},"PeriodicalIF":2.9,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932779","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 symmetry-breaking in the nonlinear Schrödinger equation on star graphs with inhomogeneities","authors":"Rahmi Rusin ,&nbsp;Hadi Susanto","doi":"10.1016/j.physd.2025.134889","DOIUrl":"10.1016/j.physd.2025.134889","url":null,"abstract":"<div><div>We investigate the nonlinear Schrödinger equation on a three-edge star graph, where each edge contains a localized inhomogeneity in the form of a Dirac delta linear potential. Such systems are of significant interest in studying wave propagation in networked structures, with applications in, e.g., Josephson junctions. By reducing the system to a set of finite-dimensional coupled ordinary differential equations, we derive explicit conditions for the occurrence of a symmetry-breaking bifurcation in a symmetric family of solutions. This bifurcation is shown to be of the transcritical type, and we provide a precise estimate of the bifurcation point as the propagation constant, which is directly related to the solution norm, is varied. In addition to the symmetric states, we explore non-positive definite states that bifurcate from the linear solutions of the system. These states exhibit distinct characteristics and are crucial in understanding solutions of the nonlinear system. Furthermore, we analyze the typical dynamics of unstable solutions, showing their behavior and evolution over time. Our results contribute to a deeper understanding of symmetry-breaking phenomena in nonlinear systems on metric graphs and provide insights into the stability and dynamics of such solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134889"},"PeriodicalIF":2.9,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144919847","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":"Generalizing the compressible pairwise interaction extended point-particle model","authors":"Smyther S. Hsiao,&nbsp;Frederick Ouellet,&nbsp;Jonathan D. Regele","doi":"10.1016/j.physd.2025.134907","DOIUrl":"10.1016/j.physd.2025.134907","url":null,"abstract":"<div><div>Ejecta physics plays an important role in material interfaces that are impacted by a strong shock wave. When a shock impacts a rough surface of solid material and melts it, the Richtmyer–Meshkov instability grows perturbations on the surface, which can eject particles. After release, the ejecta travel through the post-shock compressible flow. To accurately simulate a large number of ejecta particles, an Euler–Lagrange approach is preferred, which requires modeling the subgrid-scale physics involved with fluid–particle interactions. We generalize the previous work from Hsiao et al. (2023) to consider systems of moving particles subject to any loading shock. The following improvements were made: (1) Particles are allowed to move relative to each other (2) Non-planar shocks are accounted for along with allowing for variable shock speeds. The generalized algorithm was tested with particle-resolved simulations for canonical test cases. The results of these tests are discussed and analyzed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134907"},"PeriodicalIF":2.9,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988794","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":"Dynamic analysis and control of the spatiotemporal epidemic diffusion model driven by higher-order temporal networks","authors":"Linhe Zhu,&nbsp;Yi Ding","doi":"10.1016/j.physd.2025.134872","DOIUrl":"10.1016/j.physd.2025.134872","url":null,"abstract":"<div><div>Information plays a crucial role in the prevention and management of infectious diseases, but it can also potentially accelerate their spread. This study constructs multiple higher-order networks based on existing complex networks. We construct a higher-order temporal multiplex network that integrates information diffusion and epidemic spreading, based on the Unaware–Aware–Unaware–Susceptible–Exposed–Infected–Recovered–Susceptible (<span><math><mrow><mi>U</mi><mi>A</mi><mi>U</mi></mrow></math></span>-<span><math><mrow><mi>S</mi><mi>E</mi><mi>I</mi><mi>R</mi><mi>S</mi></mrow></math></span>) framework, to accurately describe the dynamic processes of information propagation and epidemic spreading. Additionally, we derive an expression for the epidemic threshold to determine the critical conditions for the epidemic outbreak. Higher-order interactions in the information dissemination layer increase the epidemic threshold, while higher-order interactions in the epidemic spread layer decrease the epidemic threshold. We further consider births and deaths and construct a <span><math><mrow><mi>S</mi><mi>E</mi><mi>I</mi><mi>R</mi><mi>S</mi></mrow></math></span> higher-order spatiotemporal network dynamics system. Subsequently, we investigate the Turing instability criteria in the higher-order system to study the pattern formation mechanisms of epidemic spreading in space. Adding lower-order interactions and reducing the order of the coupling function leads to Turing instability. The definition of the higher-order adjacency matrix and the generation method of higher-order networks significantly influence the distribution of infected individuals. Additionally, we propose an optimal control strategy under resource constraints aimed at effectively controlling epidemic spreading by adjusting isolation measures and verify its effectiveness in delaying epidemic spread. Finally, the <span><math><mrow><mi>S</mi><mi>E</mi><mi>I</mi><mi>R</mi><mi>S</mi></mrow></math></span> system can effectively accommodate China’s cumulative monkeypox infection data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134872"},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907027","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 periodic traveling wave solutions with or without phase transition to the Navier–Stokes–Korteweg and the Euler–Korteweg equations","authors":"Yoshikazu Giga,&nbsp;Takahito Kashiwabara,&nbsp;Haruki Takemura","doi":"10.1016/j.physd.2025.134852","DOIUrl":"10.1016/j.physd.2025.134852","url":null,"abstract":"<div><div>The Navier–Stokes–Korteweg and the Euler–Korteweg equations are considered in isothermal setting. These are diffuse interface models of two-phase flow. In one-dimensional setting, we show that for any period and any density average, there exists a periodic traveling wave solution with two phases having only two sharp internal layers in a periodic cell provided that the Korteweg relaxation parameter is small compared with the period. For the Euler–Korteweg equations, mass flux is allowed to be non-zero so that phase transition occurs but it is shown that for the Navier–Stokes–Korteweg equations no phase transition occurs for periodic traveling wave solution. Here, the Helmholtz (available) energy (modified by the mass flux) is assumed to be double-well type. We also show that such a periodic traveling wave solution tends to a monotone traveling wave solution as the period tends to infinity under suitable spatial translation. Our numerical experiment suggests that there is a periodic traveling wave with phase transition which is stable under periodic perturbation for small viscosity but it seems that this is a transition pattern.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134852"},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932778","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 transverse spectral instabilities to the (2+1)-dimensional Boussinesq equation","authors":"Wen-Wu Zhou,&nbsp;Shou-Fu Tian","doi":"10.1016/j.physd.2025.134891","DOIUrl":"10.1016/j.physd.2025.134891","url":null,"abstract":"<div><div>The primary objective of this study is to explore the spectral stability of one-dimensional small-amplitude periodic traveling wave solutions for the two-dimensional Boussinesq equation. This investigation offers a framework for comprehending intricate wave interactions across a diverse range of fluid systems and underscores the interaction between nonlinearity and dispersion during wave propagation. Through the analysis of the associated spectral problem, we discover that these periodic traveling waves are unstable under long-wavelength perturbations in both transverse directions. This finding implies that small disturbances can induce substantial alterations in wave propagation. Moreover, we demonstrate that perturbations that are periodic or square-integrable with zero mean in wave propagation, along with finite or short-wavelength periodic perturbations in the transverse direction, display stability. Our results establish the specific conditions under which transverse stability is ensured, thereby highlighting the significance of perturbation characteristics in determining the stability of wave solutions within the context of shallow water wave theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134891"},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902619","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}