Studies in Applied Mathematics最新文献

{"title":"Homoclinic Quasiperiodic Orbits and Emergence of Strange Nonchaotic Attractors in a Discontinuous Piecewise Smooth Map","authors":"Jicheng Duan,&nbsp;Laura Gardini,&nbsp;Zhouchao Wei,&nbsp;Iryna Sushko,&nbsp;Yiwen Chen","doi":"10.1111/sapm.70326","DOIUrl":"https://doi.org/10.1111/sapm.70326","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the formation and evolution of strange nonchaotic attractors (SNAs) in a discontinuous noninvertible piecewise-smooth map subjected to quasiperiodic forcing. The system is formulated as a two-dimensional skew-product, combining a piecewise-smooth one-dimensional base map with an irrational rotation. The notion of quasiperiodic homoclinic and heteroclinic orbits is introduced, and their potential relevance to the transition from smooth tori to SNAs is explored. Forward images of critical lines are shown to reflect key changes in the attractor and its basin, including disconnected components and the formation of holes. Discontinuities in the attractor are found to result from direct contact with the discontinuity line of the map. Through a set of representative examples, we identify three main routes to SNA formation: (i) contact between the attractor and its basin boundary leading to homoclinic orbits, (ii) contact between the attractor and a repeller, leading to homoclinic orbits, and (iii) contact between the attractor and the discontinuity set. These results clarify how different types of critical curves shape the dynamics, and contribute to the understanding of attractor evolution in discontinuous noninvertible quasiperiodically forced systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gibbons–Tsarev Type Systems and Eventual Identities","authors":"Alessandro Arsie,&nbsp;Paolo Lorenzoni,&nbsp;Sara Perletti,&nbsp;Karoline van Gemst","doi":"10.1111/sapm.70321","DOIUrl":"https://doi.org/10.1111/sapm.70321","url":null,"abstract":"<p>We show that non-diagonalizable reductions of the dKP equation associated with regular non-semisimple <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifolds cannot exist. The proof is based on the derivation and study of a generalized Gibbons–Tsarev system (gGT system) in the non-semisimple/non-diagonalizable setting. Remarkably, a class of solutions of the gGT system is defined by eventual identities of the underlying regular <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-manifold structure. Furthermore, we use these vector fields to construct integrable reductions of Pavlov's hydrodynamic chain. In this case, the corresponding solutions are defined for any choice of Jordan block structure of the operator of multiplication by an eventual identity.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conformable Logistic Dynamic Equations on Timescales","authors":"Mahammad Khuddush,&nbsp;Svetlin G. Georgiev","doi":"10.1111/sapm.70322","DOIUrl":"https://doi.org/10.1111/sapm.70322","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we study an autonomous conformable logistic dynamic equation in proportional conformable calculus on timescales. A reciprocal transformation reduces the nonlinear problem to a mixed first-order conformable equation and yields an exact representation, including the constant-coefficient solution with effective carrying capacity &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$K_{alpha }=k(1-kappa _1/r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Under the positivity condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {D}_{alpha }(t)=kappa _0+mu (t)(r-kappa _1)&gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, positive solutions are global and forward invariant. According to the relation between &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;κ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$kappa _1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, solutions converge to a positive equilibrium, exhibit algebraic extinction in the critical case, or decay exponentially. For the standard proportional choice, the critical order is &lt;span&gt;&lt;/span&gt;&lt;ma","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact Response to Perturbations and Dynamical Indicators in a Tumor-Growth Model","authors":"T. M. C. Priyanka,&nbsp;A. Gowrisankar,&nbsp;Lamberto Rondoni","doi":"10.1111/sapm.70323","DOIUrl":"https://doi.org/10.1111/sapm.70323","url":null,"abstract":"<div>\u0000 \u0000 <p>We formulate a three-dimensional tumor–immune model obtained by adding to an established tumor–host–effector system two phenomenological perturbation terms, whose signs are motivated by the reported tumor-promoting and effector-suppressing influence of regulatory B cells; their coefficients are dynamical control parameters and are not calibrated to biological rates. The perturbed and unperturbed dynamics are compared using phase portraits, Lyapunov exponents, parameter sensitivity, and multifractal indicators. Because trajectory-wise prediction is intrinsically limited in chaotic regimes and initial cell populations are only partially known, we also extend exact response theory, originally developed in nonequilibrium molecular dynamics, to the relevant non-compact positive set of populations values. Admissible initial densities are introduced to control boundary terms and ensure the validity of the exact response identity for finite-time ensemble averages. The resulting formulation quantifies both instantaneous and cumulative changes in tumor, host, and effector-cell observables under finite parameter perturbations, without requiring a small-perturbation approximation. Numerical tests verify the response identity against direct Monte Carlo propagation and assess sampling and time-discretization errors. For the parameter ranges studied, the perturbations can move the model between periodic and chaotic regimes, while ensemble averages remain considerably smoother than individual trajectories, and are capable of significant predictions. Long-time averaged responses are consistent across three admissible initial ensembles, although instantaneous dispersion can remain substantial. The analysis therefore separates attractor geometry from finite-time statistical response and provides a mathematically controlled framework for uncertainty-aware comparison of tumor-growth models, especially relevant in the potentially most interesting transients. The biological interpretation remains qualitative: The perturbation coefficients are not clinically calibrated rates, and any correspondence with regulatory B-cell biology requires independent experimental validation.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IS-PINN: A Fast and Efficient Training of Physics-Informed Neural Networks Using Invariant Subspace Reductions for Solving Nonlinear Diffusion Equations","authors":"Jiafu Pang,&nbsp;Shoufeng Shen,&nbsp;Guofu Yu,&nbsp;Junyang Zhang","doi":"10.1111/sapm.70324","DOIUrl":"https://doi.org/10.1111/sapm.70324","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose the invariant subspace physics-informed neural network (IS-PINN), a novel approach that combines the invariant subspace method (ISM) with deep learning to solve nonlinear diffusion equations. By restricting the solution to a prescribed invariant subspace spanned by exact basis functions, IS-PINN eliminates spatial dependencies and transforms the nonlinear diffusion equation into a dynamical system. The temporal coefficients are learned by a neural network with hard-constrained initial conditions via least-squares projection. We validate IS-PINN on five problems: the semilinear heat equation, the Riabouchinsky–Proudman–Johnson equation (RPJE), the porous medium equation, the quasilinear parabolic equation, and the (1+2)D reaction–diffusion equation. Numerical results demonstrate that IS-PINN outperforms standard PINNs, achieving mean relative <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$L_2$</annotation>\u0000 </semantics></math> errors of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1.43</mn>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mn>10</mn>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$1.43times 10^{-5}$</annotation>\u0000 </semantics></math>–<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1.26</mn>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mn>10</mn>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$1.26times 10^{-4}$</annotation>\u0000 </semantics></math> over five random seeds, with mean training time reduced by approximately 74%–98%.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic Diffusion Driven by Internal and External Brownian Motions","authors":"Türker Özsarı","doi":"10.1111/sapm.70327","DOIUrl":"https://doi.org/10.1111/sapm.70327","url":null,"abstract":"<p>The purpose of this paper is to introduce a stochastic version of Fokas' unified transform formula for evolution PDEs on domains with boundary. The unified transform method, also known as Fokas method, was originally developed for deterministic initial-boundary value problems and has, so far, been used primarily in deterministic settings. The modifications introduced here lead to stochastic representation formulas that can be used to define mild solutions of stochastic initial-boundary value problems and to perform regularity analysis in rough fractional Sobolev spaces, below the algebra threshold. To present the main ideas, we consider the canonical model of linear and nonlinear diffusion equations with additive noise and stochastic boundary conditions in their most elementary form. We assume that the evolution is subject both to external forcing prescribed through Dirichlet-type Brownian motion and to internal additive forcing whose temporal component is also Brownian.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70327","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Numerical Solution of the Poisson Equation in the Smoothed Particle Hydrodynamics","authors":"Matteo Antuono,&nbsp;Julien Michel,&nbsp;Salvatore Marrone","doi":"10.1111/sapm.70319","DOIUrl":"https://doi.org/10.1111/sapm.70319","url":null,"abstract":"<p>In the present work, we address some aspects related to the numerical solution of the Poisson equation within the framework of the Smoothed Particle Hydrodynamics (SPH). In this case, the Poisson equation is solved using nonlocal, kernel-based discretizations of the differential operators (i.e., gradient, divergence, and Laplacian operators) defined on scattered particle sets without topological connections. This paper clarifies two distinct sources of pressure artifacts that are often conflated in the SPH literature: (i) checkerboard-like spurious pressure modes caused by discrete operator incompatibility and pressure-velocity decoupling, and (ii) loss of accuracy due to particle disorder and kernel support truncation near boundaries. We propose diagnostics and procedures that separate these mechanisms and use representative benchmark tests to compare common SPH Poisson/Laplacian formulations in terms of robustness, convergence, and sensitivity to disorder and boundary deficiency. The resulting perspective reconciles conflicting claims and provides a theoretical guidance for practical applications.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70319","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence to Traveling Waves to a Parabolic–Parabolic Chemotaxis System on the Half Space","authors":"Lixin Meng,&nbsp;Ruiyuan Zhang","doi":"10.1111/sapm.70317","DOIUrl":"https://doi.org/10.1111/sapm.70317","url":null,"abstract":"<div>\u0000 \u0000 <p>We are interested in the nonlinear stability of traveling waves for a singular chemotaxis model on the half space with nonzero chemical diffusion. This model describes the dynamics of vascular endothelial cell density attracted by the concentration of vascular endothelial growth factor during the initiation of tumor angiogenesis. We show that under the nonzero flux boundary condition for cells and the Robin boundary condition for the chemical signal, solutions to the system with suitable initial data converge to a shifted traveling wave, whose profile and wave speed are uniquely determined by the parameters involved in the boundary conditions.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kinetic and Mean-Field Modeling of Muscular Dystrophies","authors":"Tommaso Lorenzi,&nbsp;Horacio Tettamanti,&nbsp;Mattia Zanella","doi":"10.1111/sapm.70316","DOIUrl":"https://doi.org/10.1111/sapm.70316","url":null,"abstract":"<p>We present a new class of models for assessing the cell dynamics characterizing muscular dystrophies. The proposed approach comprises a system of integro-differential equations for the statistical distributions, over a large patient cohort, of the densities of muscle fibers and immune cells implicated in muscle inflammation, degeneration, and regeneration, which underpin disease development. Considering an appropriately scaled version of this model, we formally derive, as the corresponding mean-field limit, a system of Fokker–Planck equations, from which we subsequently derive, as a macroscopic model counterpart, a system of differential equations for the mean densities of muscle and immune cells in the cohort of patients and the related variances. Then, we study long-time asymptotics for the mean-field model by determining the quasi-equilibrium cell distribution functions, which are in the form of probability density functions of inverse Gamma distributions, and proving the long-time convergence to such quasi-equilibrium distributions. The analytical results obtained are illustrated by means of a sample of results of numerical simulations. The modeling approach presented here has the potential to offer new insights into the balance between degeneration and regeneration mechanisms in the progression of muscular dystrophies, and provides a basis for future extensions, including the modeling of therapeutic interventions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70316","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70320","DOIUrl":"https://doi.org/10.1111/sapm.70320","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70320","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149099943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}