Studies in Applied Mathematics最新文献

{"title":"Issue Information-TOC","authors":"","doi":"10.1111/sapm.70032","DOIUrl":"https://doi.org/10.1111/sapm.70032","url":null,"abstract":"","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 3","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513583","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":"Dynamics Analysis for Diffusive Resource-Consumer Model With Nonlocal Discrete Memory","authors":"Haihui Wu,&nbsp;Xiaoqin Shen,&nbsp;Aili Wang,&nbsp;Qian Li","doi":"10.1111/sapm.70030","DOIUrl":"https://doi.org/10.1111/sapm.70030","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, based on the importance of consumer memory on spatial resource distribution, we propose a novel consumer-resource model that incorporates nonlocal discrete memory. By conducting thorough bifurcation and stability analysis, we determine the conditions for the occurrence of Hopf and Turing bifurcations and reveal a unique dynamic phenomenon termed Turing–Hopf bifurcation, which is uncommon in models without nonlocal discrete memory. We also show that as the memory delay increases, both the spatially nonhomogeneous periodic and steady-state solutions may vanish, and the unstable positive homogeneous steady state may regain stability. Furthermore, leveraging the theory of normal forms, we derive a new effective algorithm to determine the direction and stability of Hopf bifurcation in a model where the diffusion component incorporates an integral term with delay. In addition, we perform numerical simulations to validate our theoretical findings, particularly to assess the direction and stability of the delay-induced mode-1 Hopf bifurcation. Our new method is used for this purpose, and the results have been confirmed by rigorous numerical analysis.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143489706","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":"Sharp Rate of the Accelerating Propagation for a Recursive System","authors":"Na Li,&nbsp;Yingli Pan,&nbsp;Ying Su","doi":"10.1111/sapm.70029","DOIUrl":"https://doi.org/10.1111/sapm.70029","url":null,"abstract":"<div>\u0000 \u0000 <p>How to characterize the rate of accelerating propagation in recursive systems is a challenging topic though it has attracted great attention of theoretical and empirical ecologists. In this paper, we determine the sharp rate of accelerating propagation for a unimodal recursive system with a heavy-tailed dispersal kernel <span></span><math>\u0000 <semantics>\u0000 <mi>J</mi>\u0000 <annotation>$J$</annotation>\u0000 </semantics></math> through tracking of level sets of solutions with compactly supported initial data. It turns out that the solution level set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>λ</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$E_{lambda }(n)$</annotation>\u0000 </semantics></math> satisfies <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>λ</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∼</mo>\u0000 <msup>\u0000 <mi>e</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mi>ρ</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$J(E_lambda (n))sim e^{-rho ^* n}$</annotation>\u0000 </semantics></math> for large <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math> is the level and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ρ</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$rho ^*$</annotation>\u0000 </semantics></math> is determined by the linearized system at zero.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475574","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":"Large \u0000 \u0000 x\u0000 $x$\u0000 Asymptotics of the Soliton Gas for the Nonlinear Schrödinger Equation","authors":"Xiaofeng Han,&nbsp;Xiaoen Zhang,&nbsp;Huanhe Dong","doi":"10.1111/sapm.70027","DOIUrl":"https://doi.org/10.1111/sapm.70027","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we construct a Riemann–Hilbert problem of the soliton gas for the nonlinear Schrödinger equation, derived by taking the limit of the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> soliton solutions as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math>. The discrete spectra corresponding to the soliton solutions are located in four disjoint intervals on the imaginary axis, which are symmetric about the real axis. We analyze the large <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> asymptotics by setting the time variable <span></span><math>\u0000 <semantics>\u0000 <mi>t</mi>\u0000 <annotation>$t$</annotation>\u0000 </semantics></math> to zero. Using the Deift–Zhou nonlinear steepest-descent method, we find that the large <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> asymptotics at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$t=0$</annotation>\u0000 </semantics></math> behave differently, as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$xrightarrow infty$</annotation>\u0000 </semantics></math>, the asymptotics decays to the zero background exponentially, while as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mo>→</mo>\u0000 <mo>−</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$xrightarrow -infty$</annotation>\u0000 </semantics></math>, the leading-order term can be expressed with a Riemann-theta function of genus three. In the conclusion, we expand this case to the general <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> intervals and conjecture on the large <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> asymptotics.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143466094","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":"On a Bistable Delayed Nonlinear Reaction–Diffusion Equation for a Two-Phase Free Boundary: Semi-Wave and Its Numerical Simulation","authors":"Thanh-Hieu Nguyen","doi":"10.1111/sapm.70024","DOIUrl":"https://doi.org/10.1111/sapm.70024","url":null,"abstract":"<p>In this paper, we investigate the existence and uniqueness of the semi-wave solution to a bistable delayed reaction–diffusion equation with a double free boundary. This equation captures key features of biological systems and has broad applications in mathematical biology, including population dynamics, gene expression, virus propagation, and tumor growth. In particular, we employ the technique that was developed in the previous study by M. Alfaro et al. [<i>Proceedings of the London Mathematical Society</i> (3), 116, no. 4 (2018): 729–759], and use it to prove the existence and uniqueness of semi-wave solutions. Our results demonstrate that the semi-wave solutions depend on both the delay parameter and the free boundary condition. Additionally, we conduct numerical simulations to validate our theoretical results, and explore the effects of various parameters on the semi-wave solution and spreading speed.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438817","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":"Breather and Rogue Wave Solutions on the Different Periodic Backgrounds in the Focusing Nonlinear Schrödinger Equation","authors":"Fang-Cheng Fan,&nbsp;Wang Tang,&nbsp;Guo-Fu Yu","doi":"10.1111/sapm.70026","DOIUrl":"https://doi.org/10.1111/sapm.70026","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we construct breather and rogue wave solutions on the different periodic backgrounds in the focusing nonlinear Schrödinger equation by using the Darboux transformation. First, we present solutions of the Lax pair related to the periodic seed solutions with trivial and nontrivial phases. In this process, different from the previous approaches of employing the nonlinearization of the Lax pair or the traveling wave transformation, we mainly combine the proper assumption with the method of separation of variables. This strategy is more direct and simpler and can be extended to other nonlinear integrable equations. Second, we construct the Kuznetsov–Ma breather and the spatiotemporally periodic breather on the periodic background. Their asymptotic expressions are obtained, which can be used to show that the related nonlinear waves appear on the periodic background. The corresponding dynamical properties and evolution states are illustrated graphically. Finally, at branch points of breathers, the rogue waves on the periodic background are derived and their characteristics are analyzed. For breather and rogue wave solutions, we both investigate the relationship between parameters and solutions' structures and the limits when the elliptic modulus approach to 0 and 1. All the results in this paper might be helpful for us to understand the dynamics of breathers and rogue waves on the periodic background.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404719","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":"Rarefaction Wave Interaction and Existence of a Global Smooth Solution in the Blood Flow Model With Time-Dependent Body Force","authors":"Rakib Mondal,&nbsp; Minhajul","doi":"10.1111/sapm.70025","DOIUrl":"https://doi.org/10.1111/sapm.70025","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents the collision between two rarefaction waves for the one-dimensional blood flow model with non-constant body force. We establish the Riemann solutions using phase plane analysis, which are no longer self-similar. By employing Riemann invariants, we transform the system into a non-reducible diagonal system in Riemann invariant coordinates. This interaction problem then becomes a Goursat boundary value problem (GBVP) within the interaction region. We demonstrate that no vacuum forms within the interaction domain if the boundary data on characteristics is vacuum-free, and a vacuum only appears if the two rarefaction waves fail to penetrate each other within a finite time. Furthermore, we prove the existence and uniqueness of the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$C^1$</annotation>\u0000 </semantics></math> solution to the GBVP throughout the entire interaction region using <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>a priori</mtext>\u0000 <mspace></mspace>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$text{a priori} ; C^1$</annotation>\u0000 </semantics></math> bounds. Finally, we present the results of the interaction, showing that either the rarefaction waves completely penetrate each other or form a vacuum in the solution at a sufficiently large time during the process of penetration.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404662","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":"Asymptotic Behavior of a Degenerate Forest Kinematic Model With a Perturbation","authors":"Lu LI,&nbsp;Guillaume Cantin","doi":"10.1111/sapm.70014","DOIUrl":"https://doi.org/10.1111/sapm.70014","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the asymptotic behavior of the global solutions to a degenerate forest kinematic model, under the action of a perturbation modeling the impact of climate change. In the case where the main nonlinear term of the model is monotone, we prove that the global solutions converge to a stationary solution, by showing that the Lyapunov function derived from the system satisfies a Łojasiewicz–Simon gradient inequality. We also present an original algorithm, based on the Statistical Model Checking framework, to estimate the probability of convergence toward nonconstant equilibria. Furthermore, under suitable assumptions on the parameters, we prove the continuity of the flow and of the stationary solutions with respect to the perturbation parameter. Then, we succeed in proving the robustness of the weak attractors, by considering a weak topology phase space and establishing the existence of a family of positively invariant regions. At last, we present numerical simulations of the model and explore the behavior of the solutions under the effect of several types of perturbations. We also show that the forest kinematic model can lead to the emergence of chaotic patterns.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143389181","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":"Detecting (the Absence of) Species Interactions in Microbial Ecological Systems","authors":"Thomas Beardsley,&nbsp;Megan Behringer,&nbsp;Natalia L. Komarova","doi":"10.1111/sapm.70009","DOIUrl":"https://doi.org/10.1111/sapm.70009","url":null,"abstract":"<div>\u0000 \u0000 <p>Microbial communities are complex ecological systems of organisms that evolve in time, with new variants created, while others disappear. Understanding how species interact within communities can help us shed light into the mechanisms that drive ecosystem processes. We studied systems with serial propagation, where the community is kept alive by taking a subsample at regular intervals and replating it in fresh medium. The data that are usually collected consist of the % of the population for each of the species, at several time points. In order to utilize this type of data, we formulated a system of equations (based on the generalized Lotka–Volterra model) and derived conditions of species noninteraction. This was possible to achieve by reformulating the problem as a problem of finding feasibility domains, which can be solved by a number of efficient algorithms. This methodology provides a cost-effective way to investigate interactions in microbial communities.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380161","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":"Smoothing of the Higher-Order Stokes Phenomenon","authors":"Chris J. Howls,&nbsp;John R. King,&nbsp;Gergő Nemes,&nbsp;Adri B. Olde Daalhuis","doi":"10.1111/sapm.70008","DOIUrl":"https://doi.org/10.1111/sapm.70008","url":null,"abstract":"<p>For over a century, the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. In 1989, Berry demonstrated it is possible to smooth this discontinuity in broad classes of problems with the prefactor for the exponentially small contribution switching on/off taking a universal error function form. Following pioneering work of Berk, Nevins, and Roberts and the Japanese school of formally exact asymptotics, the concept of the higher-order Stokes phenomenon was introduced, whereby the ability for the exponentially small terms to cause a Stokes phenomenon may change, depending on the values of parameters in the problem, corresponding to the associated Borel-plane singularities transitioning between Riemann sheets. Until now, the higher-order Stokes phenomenon has also been treated as a discontinuous event. In this paper, we show how the higher-order Stokes phenomenon is also smooth and occurs universally with a prefactor that takes the form of a new special function, based on a Gaussian convolution of an error function. We provide a rigorous derivation of the result, with examples spanning the gamma function, a second-order nonlinear ODE, and the telegraph equation, giving rise to a ghost-like smooth contribution present in the vicinity of a Stokes line, but which rapidly tends to zero on either side. We also include a rigorous derivation of the effect of the smoothed higher-order Stokes phenomenon on the individual terms in the asymptotic series, where the additional contributions appear prefactored by an error function.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380162","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}