Mathematical Methods in the Applied Sciences最新文献

{"title":"Existence and Stability of Traveling Wavefronts in a Diffusive Vector Disease Model With Nonlocal Distributed Delay","authors":"Cun-Hua Zhang,&nbsp;Xiang-Ping Yan","doi":"10.1002/mma.70796","DOIUrl":"https://doi.org/10.1002/mma.70796","url":null,"abstract":"<div>\u0000 \u0000 <p>This article is concerned with the traveling wave front solutions of a vector disease model with a nonlocal distributed delay incorporated as an integral convolution over all past time and the whole one-dimensional spatial domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{R} $$</annotation>\u0000 </semantics></math>. In the situation when the delay kernel is assumed to be the strong generic kernel and the kernel parameter is sufficiently small, the existence and the exponential stability of traveling wavefront solutions are separately established by using the linear chain techniques and the geometric singular perturbation theory, as well as the comparison principle and the weighted energy estimates in a suitable weighted space.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14486-14501"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696615","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":"Effects of Random Diffusion and Advection on a Predator–Prey Model","authors":"Yu-Xia Wang,&nbsp;Peng-Xiang Zhang","doi":"10.1002/mma.70799","DOIUrl":"https://doi.org/10.1002/mma.70799","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we investigate the steady state problem of a predator–prey model incorporating random diffusion and advection under homogeneous Dirichlet boundary conditions. To gain a better understanding of random diffusion and advection, the stability of semitrivial steady state solutions, the nonexistence and existence of positive steady-state solutions are given. The results indicate that diffusion has a significant influence on both the stability of semitrivial steady state solutions and the coexistence region. In particular, a small positive advection coefficient reduces the size of the coexistence region, whereas a large positive advection coefficient may lead to bistable phenomena. Moreover, as other parameters vary, the stability of one semitrivial steady state solution may change at least twice.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14432-14456"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696533","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 High-Order Reaction-Diffusion Coupled System for Super-Resolution","authors":"K. Jenkal,&nbsp;Z. Zaabouli,&nbsp;L. Afraites,&nbsp;A. Laghrib","doi":"10.1002/mma.70786","DOIUrl":"https://doi.org/10.1002/mma.70786","url":null,"abstract":"<div>\u0000 \u0000 <p>Super-resolution (SR) remains a critical challenge in imaging science, particularly in applications demanding fine-texture reconstruction and noise suppression. In this work, we introduce a novel nonvariational anisotropic diffusion model, formulated as a high-order nonlinear reaction-diffusion system, designed to enhance SR capabilities. Our approach utilizes a decomposition strategy based on the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}^{-1} $$</annotation>\u0000 </semantics></math> norm, which effectively captures and preserves fine details and intricate textures in images. Theoretical analysis establishes the well-posedness of the model via the Schauder fixed-point theorem, ensuring mathematical rigor. To validate its performance, we implement a finite difference numerical scheme, testing the model against state-of-the-art SR techniques on challenging image datasets. Results demonstrate significant improvements in texture restoration, edge sharpness, and robustness to noise and degradation, surpassing competitive methods. This research lays the foundation for advanced PDE-based SR frameworks, offering significant potential for applications in biomedical imaging, satellite vision, and high-fidelity computational photography.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14524-14547"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696609","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":"Bifurcation Dynamics of a Pest Management System With Cooperative Predation, Fear Effect, and Impulsive Density-Dependent Nonlinear Effects","authors":"Zeli Zhou,&nbsp;Jianjun Jiao,&nbsp;Bingying Gao","doi":"10.1002/mma.70785","DOIUrl":"https://doi.org/10.1002/mma.70785","url":null,"abstract":"<div>\u0000 \u0000 <p>Effective integrated pest management should control pests while safeguarding the environment and human health. This study proposes a novel pest management system incorporating cooperative predation, fear effect, impulsive density-dependent nonlinear prey (pest) trapping and predator (natural enemy) release. The conditions for global asymptotic stability of the prey extinction periodic solution and system permanence are established. A supercritical bifurcation occurs when the impulsive control period serves as a bifurcation parameter. This implies that a transition from a prey extinction periodic solution to a positive periodic solution of prey–predator coexistence when the impulsive period exceeds a critical value. Meanwhile, simulations are conducted to verify the theoretical results, determine the key factors influencing pest extinction threshold condition, and explore the complex dynamics of the system. This analysis will aid future research and the development of effective pest control strategies.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14335-14354"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696062","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":"Deep Neural Network Analysis and Optimal Control for a Fractional-Order Model of HPV and Cervical Cancer","authors":"A. El-Mesady,&nbsp;M. A. Abdelkawy,&nbsp;Muhammad Farhan,&nbsp;Mohammad Izadi","doi":"10.1002/mma.70741","DOIUrl":"https://doi.org/10.1002/mma.70741","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Leveraging the Liouville–Caputo fractional derivative (LCFD), this work constructs a mathematical framework to examine the dynamics of Human Papillomavirus (HPV) transmission and its progression into cervical cancer. We propose a novel fractional-order model (FOM) consisting of five coupled fractional differential equations (FDEs) that represent different population compartments and incorporate essential epidemiological characteristics of HPV infection. To ensure mathematical validity, we rigorously prove that the model's solutions exist, are unique, and remain positive and bounded. Our analysis involves deriving the basic reproduction number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to establish a threshold for disease persistence, followed by a comprehensive examination of the stability of the disease-free and endemic equilibrium states. Parameter sensitivity analysis identifies key factors influencing disease transmission dynamics. An extension of our framework involves the formulation of a fractional optimal control problem (FOCP), which includes three time-dependent control measures: safe sexual practice promotion (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}_1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), vaccination and immunity enhancement (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}_2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), and comprehensive cancer screening and treatment implementation (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {u}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;). By employing Pontryagin's Maximum Principle (PMP), we rigorously derive the set of necessary conditions required for optimal control. T","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14563-14600"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696317","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":"T(w)o Patch or Not T(w)o Patch: A Novel Biocontrol Model","authors":"Urvashi Verma,&nbsp;Aniket Banerjee,&nbsp;Rana D. Parshad","doi":"10.1002/mma.70800","DOIUrl":"https://doi.org/10.1002/mma.70800","url":null,"abstract":"<p>A number of top-down biocontrol models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest-dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest-dependent monotone functional response is introduced into a “patch” such as a prairie strip with AF, and then disperses or drifts into a neighboring “patch” such as a crop field, to target a pest. We show that the pest extinction state is attainable in the crop field and can be globally attracting. The AF model with a patch structure can eliminate predator explosion present therein and can keep pest densities lower than the classical top-down biocontrol model. We provide the first proof of the global stability of the interior equilibrium for the classical AF model. We also observe “patch-specific chaos” – the pest occupying the crop field can oscillate chaotically, while the pest in the prairie strip oscillates periodically. We discuss these results in light of biocontrol strategies that utilize state-of-the-art farming practices such as prairie strips and drift and dispersal pressures driven by climate change.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14697-14743"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70800","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalized Solutions for Fractional Kirchhoff–Choquard Equations","authors":"Zhenyu Guo,&nbsp;Tongtong Guo","doi":"10.1002/mma.70798","DOIUrl":"https://doi.org/10.1002/mma.70798","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study a class of fractional Kirchhoff-Choquard equations with fixed mass constraints in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^3 $$</annotation>\u0000 </semantics></math>. Based on the Pohozaev manifold, by establishing the compactness lemma of the Palais–Smale sequence and using Ekeland variational principle, the existence of solutions is obtained and their asymptotic behavior is analyzed for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>∈</mo>\u0000 <mfenced>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ sin left(frac{3}{4},1right) $$</annotation>\u0000 </semantics></math>. Through variable substitution, the low-order fractional Kirchhoff equation is transformed into an equivalent system. Combining fractional inequalities and variational methods, the existence of solutions is obtained for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>∈</mo>\u0000 <mfenced>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mfrac>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ sin left(0,frac{3}{4}right] $$</annotation>\u0000 </semantics></math>.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14502-14523"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696616","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":"Non-Stationary Helical 3D Rivulet-Flows of Viscous-Plastic Incompressible Non-Newtonian Fluid","authors":"S. V. Ershkov,&nbsp;E. S. Baranovskii,&nbsp;A. V. Yudin","doi":"10.1002/mma.70747","DOIUrl":"https://doi.org/10.1002/mma.70747","url":null,"abstract":"<div>\u0000 \u0000 <p>The novel case of nonstationary flows of <i>helical type</i> governed by gravity-driven viscous-plastic flow dynamics derived for incompressible non-Newtonian fluid is investigated here analytically in case of given (constant) value of <i>Bernoulli</i>-function. In such types of flow, the velocity is linearly and spatially dependent on curl field. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained. Equations of momentum, continuity, and that one for the components of stress tensor are studied. The spatial and time-dependent structure of pressure field of the fluid flow should be determined via constant <i>Bernoulli</i>-function if components of the velocity of the flow are already obtained. It is remarkable that the case of non-stationary <i>helical</i> or <i>Beltrami</i> flow for incompressible gravity-driven viscous-plastic flow governed by three-dimensional equations has been investigated for the first time to the best of our knowledge.</p>\u0000 <p><b>MSC Classification:</b> 35Q35, 76D17</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14382-14392"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696402","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":"2D Impulsive Pseudoparabolic Equations With the Volterra-Type and Fredholm-Type Initial Layers","authors":"Stanislav Antontsev,&nbsp;Ivan Kuznetsov,&nbsp;Sergey Sazhenkov","doi":"10.1002/mma.70792","DOIUrl":"https://doi.org/10.1002/mma.70792","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the two-dimensional Cauchy–Dirichlet problems for the quasilinear pseudoparabolic integro-differential Volterra equation and for the quasilinear pseudoparabolic integro-differential Fredholm equation. In each of these two problems, the integral term depends on a positive integer parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math> and, as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$$ nto +infty $$</annotation>\u0000 </semantics></math>, converges weakly<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow></mrow>\u0000 <mrow>\u0000 <mo>⋆</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {}^{star } $$</annotation>\u0000 </semantics></math> to the expression incorporating the Dirac delta-function, which models an instantaneous impulsive impact. For fixed <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>ℕ</mi>\u0000 </mrow>\u0000 <annotation>$$ nin mathbb{N} $$</annotation>\u0000 </semantics></math> we prove the well-posedness of each of the two problems in the class of regular weak solutions. Further, for each of the two problems, we establish that the initial shock layer, associated with the Dirac delta-function, is formed as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$$ nto +infty $$</annotation>\u0000 </semantics></math>, and that the family of regular weak solutions of the original problem converges to the strong solution of a limit two-scale microscopic–macroscopic model.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14457-14485"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696312","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":"Dynamical Analysis of A Predator-Prey Model Incorporating Allee Effect and Mutual Interference Between Predators","authors":"Chenyu Wang,&nbsp;Wensheng Yang","doi":"10.1002/mma.70788","DOIUrl":"https://doi.org/10.1002/mma.70788","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we put forward and study a modified Leslie-Gower predator-prey model with Crowley-Martin functional response and Allee effect in the growth rate of a predator population. Crowley–Martin-type functional response is considered to describe mutual interference between predators. Our analysis shows that the intensity of Allee effect affect the stability of all equilibria, and by plotting the two-parameter bifurcation diagram of the degree of mutual interference between predators and the intensity of Allee effect, it is found that under their influence, the system will appear Bi-stable phenomenon. In addition, by considering the intensity of Allee effect as a bifurcation parameter, the one-parameter bifurcation diagram of the predator appears saddle-node bifurcation and Hopf bifurcation. Finally, Turing instability occurs in the reaction-diffusion system. The study reveals that as the intensity of the Allee effect increases, predators face greater survival pressure, their population growth becomes limited, predation patterns changes, the distribution of the prey population changes, and low-density areas of the prey decrease. As mutual interference between predators increases, the distribution patterns of both predators and prey shift significantly. High interference reduces high-density prey clusters, while predator distribution, though fluctuating, becomes smoother overall. This study highlights the complex interaction between Allee effect and predator-predator interaction in predator-prey dynamics. The results may provide biological insights and ecological management suggestions for predator-prey interaction.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14393-14419"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696400","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}