Physica D: Nonlinear Phenomena最新文献

{"title":"Frequency-domain computation of Lyapunov-Perron transformation with detection of quasi-periodic solution bifurcation","authors":"Yanmao Chen,&nbsp;Jike Liu","doi":"10.1016/j.physd.2025.134765","DOIUrl":"10.1016/j.physd.2025.134765","url":null,"abstract":"<div><div>Lyapunov-Perron (LP) transformation is well-known as an indispensible technique to reduce a linear quasi-periodic (QP) system, under certain conditions, into a time-invariant one, which we call the reduced system. The reducibility of QP system received a lot of qualitative studies, however quite few research focused on the quantification of the LP transformation itself. The major obstacle probably consists in the calculation of a QP matrix describing the transformation. In this study we will propose a semi-analytical approach, based on frequency-domain analysis, to determine the LP transformation precisely and efficiently. Our approach is divided into two steps. Firstly a constant matrix is determined to represent the reduced system, utilizing the circularly distributed multipliers of the QP system provided by a frequency-domain approach established recently by the authors. With the constant matrix, a linear and solvable QP system governing the transformation matrix is deduced and solved via harmonic balancing, in which the harmonic coefficients are provided by linear algebraic equations. Numerical examples show the semi-analytical results are very accurate for both the constant and the QP matrix, representing the reduced system and the LP transformation, respectively.</div><div>As an application, the proposed approach provides us with a convenient way to detect the bifurcation types of QP responses. For instance, the harmonic components of the QP matrix are analyzed for distinguishing saddle-node and symmetry-breaking bifurcations. For a special example where the QP system cannot be reduced via the routine LP transformation, interestingly, it turns out the system reduction can still be realized via an extended transformation. The harmonic components of the QP matrix in the extended transformation can also identify period-doubling bifurcation. Lastly the proposed approach is shown to be capable of detecting QP Hopf bifurcation, exemplified by a van der Pol-Rossler coupled system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134765"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205396","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":"Four-equation model for unified prediction of turbulent mixing induced by interfacial instabilities","authors":"Rui-han Zhao ,&nbsp;Han-song Xie ,&nbsp;Meng-juan Xiao ,&nbsp;Yu-hui Wang ,&nbsp;You-sheng Zhang","doi":"10.1016/j.physd.2025.134724","DOIUrl":"10.1016/j.physd.2025.134724","url":null,"abstract":"<div><div>Turbulent mixing induced by interfacial instabilities are generally predicted using the Reynolds-averaged Navier–Stokes (RANS) model in practical applications. Among RANS models, the advanced Besnard–Harlow–Rauenzahn (BHR) series stand out due to its capacity to characterize the mixing state, which is quite important for reaction rate calculation in fusion engineering. However, the present limitation of this model is its inability to unified predict mixing growth rates and profiles across diverse density ratios or types of turbulent mixing scenarios. To overcome these limitations, we extend the methodology in determining turbulence model coefficients to the four-equation framework. The extension concerns a refined four-equation model, particularly in modifying the dissipation term associated with the density-specific volume covariance, thereby greatly improving the model’s performance at high density ratios. Further, new self-similar profiles for various physical quantities are introduced by considering more realistic evolution. This enhancement is shown to yield more plausible predictions. Finally, leveraging the unique traits of the four-equation model, we utilize an ansatz of self-similarity to derive consistent model coefficients ensemble tailored to different turbulent mixing scenarios. With these enhancements, this model realizes unified predictions of mixing width and profiles across classical turbulent mixings and complex mixings, agreeing well with high-fidelity numerical simulations and experimental measurements. Given the model’s descriptive prowess of mixing state characteristics pertinent to engineering challenges, it has significant potential in the precise prediction of fusion reaction rate and assessments of fusion performance.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134724"},"PeriodicalIF":2.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178727","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":"Long-time dynamics of a parabolic-ODE SIS epidemic model with saturated incidence mechanism","authors":"Rui Peng ,&nbsp;Rachidi Salako ,&nbsp;Yixiang Wu","doi":"10.1016/j.physd.2025.134747","DOIUrl":"10.1016/j.physd.2025.134747","url":null,"abstract":"<div><div>In this paper, we investigate a parabolic-ODE SIS epidemic model with no-flux boundary conditions in a heterogeneous environment. The model incorporates a saturated infection mechanism <span><math><mrow><mi>S</mi><mi>I</mi><mo>/</mo><mrow><mo>(</mo><mi>m</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>S</mi><mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>m</mi><mo>≥</mo><mo>,</mo><mspace></mspace><mo>⁄</mo><mo>≡</mo><mn>0</mn></mrow></math></span>. This study is motivated by disease control strategies, such as quarantine and lockdown, that limit population movement. We examine two scenarios: one where the movement of the susceptible population is restricted, and the other where the movement of the infected population is neglected. We establish the long-term dynamics of the solutions in each scenario. Compared to previous studies that assume the absence of a saturated incidence function (i.e., <span><math><mrow><mi>m</mi><mo>≡</mo><mn>0</mn></mrow></math></span>), our findings highlight the novel and significant interplay between total population size, transmission risk level, and the saturated incidence function in influencing disease persistence, extinction, and spatial distribution. Numerical simulations are performed to validate the theoretical results, and the implications of the results are discussed in the context of disease control and eradication strategies.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134747"},"PeriodicalIF":2.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205649","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":"Assessment of anti-jamming capabilities in infrared-guided missile systems","authors":"Xinyan Li ,&nbsp;Sange Li ,&nbsp;Zhaoxing Gao","doi":"10.1016/j.physd.2025.134737","DOIUrl":"10.1016/j.physd.2025.134737","url":null,"abstract":"<div><div>Missiles possess immense destructive power and play a decisive role in determining military strength in conflicts. Existing research predominantly focuses on the guidance system level, evaluating missile anti-jamming performance based on the overall missile system and often using anti-jamming probability as the sole metric. However, this approach lacks systematic investigation into the anti-jamming process. To address this gap, this paper establishes a multi-level evaluation system for infrared guided missile, analyzing the missile overall system, guidance system, seeker, and external environment. By employing the Fuzzy Analytic Hierarchy Process (Fuzzy AHP), weight coefficients for each component are calculated using a fuzzy judgment matrix, enabling a comprehensive evaluation and the construction of a multi-level evaluation index system. Simulation experiments were conducted to validate the model’s effectiveness. Using the Latin Hypercube Sampling (LHS) algorithm, approximately 1,000 scenarios capturing the essential characteristics of missile anti-jamming were generated, reducing computational time by around 80% while maintaining accuracy. Experimental results demonstrated a recognition probability exceeding 85% and average miss distances within acceptable limits. Both static and dynamic validation confirmed the model’s robustness, proving its ability to accurately predict missile anti-jamming performance under various conditions. This study provides a solid foundation for future research and improvements in missile anti-jamming systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134737"},"PeriodicalIF":2.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194494","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":"Topological horseshoe and uniform hyperbolicity of the symplectic coupled Hénon map","authors":"Keisuke Fujioka ,&nbsp;Ryota Kogawa ,&nbsp;Jizhou Li ,&nbsp;Akira Shudo","doi":"10.1016/j.physd.2025.134722","DOIUrl":"10.1016/j.physd.2025.134722","url":null,"abstract":"<div><div>We analyze the topological horseshoe and the uniform hyperbolicity of a four-dimensional symplectic map, which is introduced by coupling two two-dimensional symplectic Hénon maps via linear terms. Based on the cone field argument following Devaney and Nitecki <span><span>[1]</span></span>, we first derive a sufficient condition for topological horseshoe and uniform hyperbolicity in the parameter space including the two different anti-integrable limits. We then explore uniformly hyperbolic parameter regions by applying the computer-assisted proof developed by Arai and find that there exist non-trivial uniformly hyperbolic regions in the parameter space that differ from those obtained using the cone condition. The existence of such non-trivial uniformly hyperbolic regions reminds us of the so-called hyperbolic plateaus in the two-dimensional Hénon map.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134722"},"PeriodicalIF":2.7,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205652","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-through problem for a Jeffreys type viscoelastic fluid","authors":"Evgenii S. Baranovskii","doi":"10.1016/j.physd.2025.134726","DOIUrl":"10.1016/j.physd.2025.134726","url":null,"abstract":"<div><div>We investigate a nonlinear boundary value problem describing the steady-state flow of an incompressible viscoelastic fluid of Jeffreys type through a 3D (or 2D) bounded domain. On the flow domain boundary, inhomogeneous Dirichlet conditions are stated for the flow velocity. Both the weak and strong formulations of this problem are considered. Using the vanishing artificial viscosity method and an existence result from the Leray–Schauder theory of topological degree, we construct a weak solution. Notably, the existence theorem, proved in the framework of the weak formulation, does not necessitate smallness assumptions on forcing and boundary data. It is established that the weak solutions set is sequentially weakly closed. We also obtain sufficient conditions for the existence and coincidence of strong solutions. Moreover, we analyzed the convergence of the constructed solutions when the stress relaxation and retardation times simultaneously tend to zero.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134726"},"PeriodicalIF":2.7,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222001","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":"Group-convolutional extended dynamic mode decomposition","authors":"Hans Harder ,&nbsp;Feliks Nüske ,&nbsp;Friedrich M. Philipp ,&nbsp;Manuel Schaller ,&nbsp;Karl Worthmann ,&nbsp;Sebastian Peitz","doi":"10.1016/j.physd.2025.134725","DOIUrl":"10.1016/j.physd.2025.134725","url":null,"abstract":"<div><div>This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by finite-dimensional surrogates, e.g., via extended dynamic mode decomposition (EDMD), is challenging for high-dimensional systems due to computational constraints. To tackle this problem with a particular focus on EDMD, we demonstrate – under suitable equivariance assumptions on the system and the observables – that the optimal EDMD matrix is equivariant. That is, its action on states can be described by group convolutions and the generalized Fourier transform. We show that this structural property has many advantages for equivariant systems, in particular, that it allows for data-efficient learning, fast predictions and fast eigenfunction approximations. We conduct numerical experiments on the Kuramoto–Sivashinsky equation and a <span><math><mi>λ</mi></math></span>-<span><math><mi>ω</mi></math></span> spiraling wave system, both nonlinear partial differential equations, providing evidence of the effectiveness of this approach, and highlighting its potential for broader applications in dynamical systems analysis.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134725"},"PeriodicalIF":2.7,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169786","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":"The unified transform method to the Hirota equation with periodic initial condition","authors":"Leilei Liu ,&nbsp;Jian Xu ,&nbsp;Weiguo Zhang ,&nbsp;Liuyong Pang ,&nbsp;Zhenkun Zhang","doi":"10.1016/j.physd.2025.134720","DOIUrl":"10.1016/j.physd.2025.134720","url":null,"abstract":"<div><div>In this paper, we study the Hirota equation with periodic initial conditions via the unified transform method(UTM) extended by Fokas and Lenells. For nonlinear integrable evolution equations, the UTM expresses the solution in terms of a matrix Riemann-Hilbert problem. The associated jump matrices are computed in terms of the initial conditions and all boundary values. However, it is quite difficult to obtain all the initial conditions and boundary value data. It is known that the solution of the initial boundary value problem on a finite interval with <span><math><mi>x</mi></math></span>-periodic boundary conditions, can be regarded as the initial value problem on a circle. For the Hirota equation with periodic initial condition, we show that the solution can be explicitly expressed based on the initial data alone. Furthermore, the explicit solution is obtained, which corresponds to one-gap solution.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134720"},"PeriodicalIF":2.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116704","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":"Magnetic wave dynamics in ferromagnetic thin films: Interactions of solitons and positons in Landau–Lifshitz–Gilbert equation","authors":"Riaz Ur Rahman ,&nbsp;Zaidong Li ,&nbsp;Jingsong He","doi":"10.1016/j.physd.2025.134719","DOIUrl":"10.1016/j.physd.2025.134719","url":null,"abstract":"<div><div>This study explores the higher-order soliton and smooth positon solutions derived from the Landau–Lifshitz–Gilbert (LLG) equation which describes the wave propagation in the physical setting of ferromagnetic thin films by adopting the Darboux transformation (DT) technique. The LLG equation is reformulated into an integrable nonlinear Schrödinger-like equation under the long-wave approximation. This approach facilitates the analysis of the propagation and interaction of magnetic solitons and positons within a ferromagnetic thin films, by taking into account the effects of interfacial Dzyaloshinskii–Moriya (DM) interaction. The DM interaction notably influences the soliton and positon velocities, alters their collision positions, and impacts their propagation trajectories. The magnetization dynamics, described by <span><math><mrow><mover><mrow><mi>m</mi></mrow><mo>→</mo></mover><mo>=</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>x</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>y</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>y</mi></mrow></msub><mo>+</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>z</mi></mrow></msub></mrow></math></span>, exhibits distinct characteristics where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span> represent oscillations in the plane perpendicular to the external field with breather-like properties, while <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span> forms localized magnetized states. The magnetization dynamics are characterized through Bloch sphere trajectories, revealing progressively localized spiral patterns for first- and second-order soliton and positon solutions, indicating enhanced spatial confinement of magnetic moments. Moreover, the dynamic behavior of smooth positons within the NLS-type equation is studied using the decomposition method of the modulus square. This methodology offers an approximate characterization of positon trajectories and the time-dependent “phase shift” occurring after collisions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134719"},"PeriodicalIF":2.7,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116707","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":"Evaluation of probability density function descriptions for three-component Rayleigh–Taylor mixing","authors":"Kevin Ferguson,&nbsp;Brandon E. Morgan","doi":"10.1016/j.physd.2025.134717","DOIUrl":"10.1016/j.physd.2025.134717","url":null,"abstract":"<div><div>Results from simulations of a three-component Rayleigh–Taylor (RT) mixing problem are presented. These simulations are conducted in heavy–light–heavy and heavy–intermediate–light configurations, and each of these configurations are further considered in high- and low-Reynolds-number regimes. This results in RT-unstable flow with one or both interfaces initially unstable, permitting the influence of problem configuration on the statistical description of three-component RT-driven mixing to be considered. Mass fraction covariances are observed to undergo a sign change through the mixing layer in all four configurations considered. This appears to be unique to the multi-component case and represents another way in which multi-component RT mixing differs from the two-component case. Qualitative and quantitative comparisons of joint and marginal probability density function (PDF) descriptions of species concentration are made. Three-, five-, and six-parameter model PDFs are compared against simulation data to assess how accurately they describe the mixing, and it is found that three-component mixing requires at least a five-parameter model PDF to accurately describe the mixing. Notably, the marginal distributions of three-component mixing do not appear to conform to a beta distribution, representing a departure from the classical two-component RT case. Statistical neutrality also appears to influence the optimal choice of model PDF, which is found to be a function of problem configuration.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134717"},"PeriodicalIF":2.7,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107140","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}