数学最新文献

{"title":"Finite-Agent Stochastic Differential Games on Large Graphs: I. The Linear-Quadratic Case","authors":"Ruimeng Hu,&nbsp;Jihao Long,&nbsp;Haosheng Zhou","doi":"10.1007/s00245-025-10309-8","DOIUrl":"10.1007/s00245-025-10309-8","url":null,"abstract":"<div><p>In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to previous works, our model offers a more realistic depiction of strategic decision-making processes. For general graphs, we establish the convergence of fictitious play, a widely-used iterative solution method for determining the Nash equilibrium of our proposed game model. Notably, under appropriate conditions, this convergence holds true irrespective of the number of players involved. For vertex-transitive graphs, we develop a semi-explicit characterization of the Nash equilibrium. Through rigorous analysis, we demonstrate the well-posedness of this characterization under certain conditions. We present numerical experiments that validate our theoretical results and provide insights into the intricate relationship between various game dynamics and the underlying graph structure.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929361","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":"From invasion to coexistence: A mathematical modeling approach to predator–prey dynamics under invasive pressure","authors":"Dipam Das ,&nbsp;Debasish Bhattacharjee ,&nbsp;Changjin Xu","doi":"10.1016/j.chaos.2025.117126","DOIUrl":"10.1016/j.chaos.2025.117126","url":null,"abstract":"<div><div>Biological invasion stands out as one of the most crucial ecological phenomena within an ecosystem. Invasion indicates the phenomenon in which a novel species infiltrates a pre-existing ecosystem. Invasive predator species present considerable challenges to native ecosystems, frequently altering established predator–prey relationships. Driven by empirical observations and a conspicuous lack of comprehensive mathematical modeling in the context of ecological invasions, this study formulates and examines a mathematical model that represents the ecological dynamics in a post-invasion context, featuring two predator species – one native and one invasive – alongside a common prey species. The model integrates essential ecological processes, including the utilization of prey refuges to evade native predators, prey naivety toward invasive predators, the counter-attack strategies employed by prey, interspecific competition among predators, the reintroduction or migration of native predators, environmental challenges impacting invasive predators, and the harvesting efforts aimed at controlling the invasive species. We have conducted rigorous stability and bifurcation analyses, including two-parametric bifurcation analysis, to gain insights into the system dynamics. Detailed numerical simulations are conducted to explore the impacts of reintroducing or migrating native predators and various other parameters on the long-term effects of invasion, including conditions for species coexistence, invasion failure, and the extinction of native predators. The results of our study yield fresh theoretical perspectives on the processes that influence post-invasion dynamics, while also suggesting possible approaches for managing the effects of invasive predators on native ecosystems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117126"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Artificial neural network estimation for heated convective Carreau nanofluid model under the influence of magnetic, heat source/sink and cross diffusions over an exponentially stretching sheet","authors":"N.A. Shah ,&nbsp;Khalid Masood ,&nbsp;Zeeshan ,&nbsp;Naqqash Dilshad","doi":"10.1016/j.chaos.2025.117171","DOIUrl":"10.1016/j.chaos.2025.117171","url":null,"abstract":"<div><div>This study provides a robust artificial neural network (ANN) framework for the predictive estimation of a heated convective Carreau nanofluid model (HCCNFM) affected by magnetic, heat generation/absorption, and cross-diffusion through an exponentially extending surface. The governing physical characteristics is described via a set of coupled, nonlinear partial differential equations (PDEs), that are deliberately reduced to a structure of ordinary differential equations (ODEs) via resemblance transformations to facilitate numerical modeling. The resulting boundary value problem has been addressed using the BVP4C technique in MATLAB program to get high-fidelity datasets which includes velocity, temperature, and concentration descriptions under different flow conditions and physical properties. These datasets are then used to train, validate, and test using multilayer feed-forward ANN architecture, designed with the Levenberg–Marquardt algorithm (LMA). The efficiency of the ANN model is meticulously assessed through multiple statistical metrics, such as mean square error (MSE), histogram errors (HE), regression plots, autocorrelation, and function fitting analysis. The prediction error is observed between 10⁻⁴ and 10⁻⁶ which confirm the accuracy of ANN-LMA model. It is observed that velocities of HCCNFM declines as the <span><math><mi>M</mi></math></span> increases while enhances for <span><math><mi>W</mi><msub><mi>e</mi><mn>1</mn></msub></math></span> and <span><math><mi>W</mi><msub><mi>e</mi><mn>2</mn></msub></math></span> for both shear-thinning and shear-thickening fluids. The HCCNFM temperature exhibits opposite trend for <span><math><mi>Q</mi><mo>&gt;</mo><mn>0</mn></math></span> and <span><math><mi>Q</mi><mo>&lt;</mo><mn>0</mn></math></span> for both shear-thinning and shear-thickening fluids. This hybrid numerical-ANN approach highlights significant potential for applications in thermal treatment, polymeric extrusion, and bioengineering mechanisms involving smart fluids.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117171"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fixed-time control of nonlinear systems with time-varying gains: A novel stability criterion","authors":"Xuelian Wang ,&nbsp;Lin Sun ,&nbsp;Yu-Long Wang","doi":"10.1016/j.chaos.2025.117082","DOIUrl":"10.1016/j.chaos.2025.117082","url":null,"abstract":"<div><div>This paper focuses on the fixed-time command-filtered tracking control problem for a class of nonlinear systems, in which a novel time-varying gain scheme, distinct from traditional time-invariant ones, is employed. Notably, an improved fixed-time stability lemma for strict-feedback nonlinear systems is constructed, which extends existing stability results by a specific variable gain function, driving the control system to a stable state within a fixed time horizon. With the help of the backstepping method, a novel fixed-time command-filtered controller incorporating a compensation mechanism is designed to mitigate errors between filter outputs and virtual control inputs. Based on the proposed lemma, the proposed control approach guarantees both fixed-time stability and precise tracking of reference signals. Finally, the effectiveness and practicality of the proposed method are demonstrated by comparative algorithm analysis and simulation studies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117082"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems","authors":"Stefano Biagi ,&nbsp;Giovanni Cupini ,&nbsp;Elvira Mascolo","doi":"10.1016/j.na.2025.113915","DOIUrl":"10.1016/j.na.2025.113915","url":null,"abstract":"<div><div>We consider a class of energy integrals, associated to nonlinear and non-uniformly elliptic equations, with integrands <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow></mrow></math></span> satisfying anisotropic <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>q</mi></mrow></math></span>-growth conditions of the form <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mo>≤</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>≤</mo><mi>μ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfenced><mrow><msup><mrow><mrow><mo>|</mo><mi>ξ</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi></mrow></msup><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>γ</mi></mrow></msup><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></math></span> for some exponents <span><math><mrow><mi>γ</mi><mo>≥</mo><mi>q</mi><mo>≥</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, and non-negative functions <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>μ</mi></mrow></math></span> subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113915"},"PeriodicalIF":1.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988180","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":"A priori estimates and large population limits for some nonsymmetric Nash systems with semimonotonicity","authors":"Marco Cirant, Davide Francesco Redaelli","doi":"10.1002/cpa.70009","DOIUrl":"https://doi.org/10.1002/cpa.70009","url":null,"abstract":"We address the problem of regularity of solutions to a family of semilinear parabolic systems of equations, which describe closed‐loop equilibria of some ‐player differential games with Lagrangian having quadratic behaviour in the velocity variable, running costs and final costs . By global (semi)monotonicity assumptions on the data and , and assuming that derivatives of in directions are of order for , we prove that derivatives of enjoy the same property. The estimates are uniform in the number of players . Such a behaviour of the derivatives of arise in the theory of Mean Field Games, though here we do not make any symmetry assumption on the data. Then, by the estimates obtained we address the convergence problem in a ‘heterogeneous’ Mean Field framework, where players all observe the empirical measure of the whole population, but may react differently from one another. We also discuss some results on the joint and vanishing viscosity limit.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity of minimal surfaces with capillary boundary conditions","authors":"Luigi De Masi, Nick Edelen, Carlo Gasparetto, Chao Li","doi":"10.1002/cpa.70008","DOIUrl":"https://doi.org/10.1002/cpa.70008","url":null,"abstract":"We prove ‐regularity theorems for varifolds with capillary boundary condition in a Riemannian manifold. These varifolds were first introduced by Kagaya–Tonegawa. We establish a uniform first variation control for all such varifolds (and free‐boundary varifolds generally) satisfying a sharp density bound and prove that if a capillary varifold has bounded mean curvature and is close to a capillary half‐plane with angle not equal to , then it coincides with a properly embedded hypersurface. We apply our theorem to deduce regularity at a generic point along the boundary in the region where the density is strictly less than 1.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"48 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spreading dynamics of a nonlocal diffusive model with a free boundary","authors":"Lei Li ,&nbsp;Mingxin Wang","doi":"10.1016/j.jde.2025.113741","DOIUrl":"10.1016/j.jde.2025.113741","url":null,"abstract":"<div><div>We study the spreading speed and asymptotic behavior of the solution to a nonlocal diffusive model with a free boundary. First, we construct a suitable lower solution to determine the exact finite spreading speed of the free boundary <span><math><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, which is also the asymptotic spreading speed of the population density <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span>. Then, we investigate the asymptotic behavior of the level set <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> of <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> and find an intriguing propagation phenomenon. Specifically, as <span><math><mi>t</mi><mo>→</mo><mo>∞</mo></math></span>, for large <em>λ</em>, the infimum of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> converges to a unique constant determined by a positive steady state, while the infimum for small <em>λ</em> and the supremum for all considered <em>λ</em> share the same spreading speed as that of <span><math><mi>h</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. Finally, when the spreading speed is infinite, a phenomenon known as accelerated spreading, we employ two lower solutions to derive the rate of accelerated spreading and the asymptotic behavior of <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> for algebraically decaying kernels.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"449 ","pages":"Article 113741"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932787","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":"Corrigendum to: “Quantization and the resolvent algebra” [J. Funct. Anal. 277 (8) (2019) 2815–2838]","authors":"Teun D.H. van Nuland,&nbsp;Lorenzo Pettinari","doi":"10.1016/j.jfa.2025.111184","DOIUrl":"10.1016/j.jfa.2025.111184","url":null,"abstract":"<div><div>In <span><span>[3]</span></span> it is claimed incorrectly that the Berezin quantization map maps surjectively to the resolvent algebra.<span><span>¹</span></span> We show here that it does not. Similarly, the Berezin map defined on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></math></span> does not reach all compact operators, contrary to what is claimed in <span><span>[2, II.(2.73)]</span></span>.<span><span>²</span></span> We moreover fill a gap in the proof of injectivity of the Berezin quantization map on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of <span><span>[3]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111184"},"PeriodicalIF":1.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933790","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":"Entire functions with Cantor bouquet Julia sets","authors":"Leticia Pardo-Simón,&nbsp;Lasse Rempe","doi":"10.1112/jlms.70142","DOIUrl":"https://doi.org/10.1112/jlms.70142","url":null,"abstract":"<p>A hyperbolic transcendental entire function with connected Fatou set is said to be of <i>disjoint type</i>. It is known that the Julia set of a disjoint-type function of finite order is a <i>Cantor bouquet</i>; in particular, it is a collection of arcs (‘hairs'), each connecting a finite endpoint to infinity. We show that the latter property is equivalent to the function being <i>criniferous</i> in the sense of Benini and Rempe (a necessary condition for having a Cantor bouquet Julia set). On the other hand, we show that there is a criniferous disjoint-type entire function whose Julia set is <i>not</i> a Cantor bouquet. We also provide a new characterisation of Cantor bouquet Julia sets in terms of the existence of certain absorbing sets for the set of escaping points, and use this to give a new intrinsic description of a class of entire functions previously introduced by the first author. Finally, the main known sufficient condition for Cantor bouquet Julia sets is the so-called <i>head-start condition</i> of Rottenfußer et al. Under a mild geometric assumption, we prove that this condition is also necessary.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70142","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934814","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}