Mathematical Methods in the Applied Sciences最新文献

{"title":"Synchronization of Caputo-Hadamard Fractional-Order Competitive Neural Networks With Discrete and Distributed Delays","authors":"Zhenzhen Zhang,&nbsp;Hong-Li Li,&nbsp;Dan-Dan Li,&nbsp;Long Zhang,&nbsp;Jinde Cao","doi":"10.1002/mma.70745","DOIUrl":"https://doi.org/10.1002/mma.70745","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the synchronization problem for Caputo–Hadamard fractional-order competitive neural networks (CHFCNNs) with both discrete and distributed delays. First, a new lemma is established by employing Caputo–Hadamard fractional calculus theory and analytical techniques. Second, an adaptive hybrid controller and a linear controller are designed. By employing inequality techniques, leveraging properties of the Mittag-Leffler function, and utilizing our established lemma, the criteria for both Mittag-Leffler synchronization and complete synchronization are derived. Finally, the validity of the theoretical results is verified through numerical examples.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13382-13400"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565132","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 Finite Iterative Algorithm for Calculating a Hermitian Solution to a Single-Variable Generalized Quaternion Matrix Equation","authors":"Ahmed M. E. Bayoumi,&nbsp;Mahmoud Saad Mehany","doi":"10.1002/mma.70719","DOIUrl":"https://doi.org/10.1002/mma.70719","url":null,"abstract":"<div>\u0000 \u0000 <p>A quaternion matrix <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$$ A $$</annotation>\u0000 </semantics></math> is called Hermitian (self-adjoint) if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>=</mo>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <mo>.</mo>\u0000 </mrow>\u0000 <annotation>$$ A={A}^{ast }. $$</annotation>\u0000 </semantics></math> This study provides a finite iterative algorithm for determining a Hermitian solution to a single-variable generalized quaternion matrix equation. Assuming consistency, the technique converges to a solution in a finite number of steps from any initial matrix, independent of round-off errors. Some lemmas and a principal theorem are investigated to build the theoretical foundation of this method. As an application of the proposed equation, we present an algorithm for finding a Hermitian solution to a quaternion matrix equation, which includes <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>η</mi>\u0000 </mrow>\u0000 <annotation>$$ eta $$</annotation>\u0000 </semantics></math>-conjugate of the unknown quaternion matrix for some <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>η</mi>\u0000 <mo>∈</mo>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 <mo>,</mo>\u0000 <mi>j</mi>\u0000 <mo>,</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mo>.</mo>\u0000 </mrow>\u0000 <annotation>$$ eta in left{boldsymbol{i},boldsymbol{j},boldsymbol{k}right}. $$</annotation>\u0000 </semantics></math> Numerical examples are provided to substantiate the efficacy of the established algorithm. These algorithms can be performed in MATLAB software through the QTFM toolbox.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13053-13067"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565143","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":"Well-Posedness and Blow-Up of Solutions to a \u0000 \u0000 \u0000 p\u0000 (\u0000 x\u0000 )\u0000 \u0000 $$ p(x) $$\u0000 -Laplacian Plate Equation With Variable-Exponent Nonlocal Damping and Logarithmic Source","authors":"Mohammad Shahrouzi,&nbsp;Zülal Mısır","doi":"10.1002/mma.70730","DOIUrl":"https://doi.org/10.1002/mma.70730","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates a class of nonlinear plate equations with the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ p(x) $$</annotation>\u0000 </semantics></math>-Laplacian operator and a nonlocal damping term in the presence of a variable-exponent logarithmic source. Using the Faedo-Galerkin approximation, we establish the existence of local weak solutions. Subsequently, after demonstrating that these local solutions extend globally in time, we prove their asymptotic stability. Finally, employing a contradiction method, we show that there exists a finite time at which the solutions blow up, provided the initial data satisfy appropriate conditions.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13123-13147"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565146","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":"Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces","authors":"Lucas da Silva,&nbsp;Marco Souto","doi":"10.1002/mma.70739","DOIUrl":"https://doi.org/10.1002/mma.70739","url":null,"abstract":"<p>This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type\u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13324-13360"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70739","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565131","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":"Impact of Quarantine and Distributed Patching on SLBQPS Computer Virus Model","authors":"K. Sunil Behal,&nbsp;Sunita Gakkhar,&nbsp;Tanuja Srivastava","doi":"10.1002/mma.70733","DOIUrl":"https://doi.org/10.1002/mma.70733","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;A nonlinear deterministic &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ SLBQPS $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; model for virus spread and patch distribution is proposed and analyzed. The impact of patching, quarantine and patch invalidation is analyzed under parametric conditions and verified by numerical simulations. It has been found that increasing the patching rate &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ beta $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; or decreasing the patch invalidation rate &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;γ&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;$$ {gamma}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; indicates that the virus has been eradicated from the network. Three basic reproduction numbers, for virus spread without quarantine, &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; with quarantine &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;mi&gt;Q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_Q $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and for patching &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;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_p $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are computed. The basic reproduction number for patching, &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 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13068-13091"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565144","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":"Mathematical Analysis of Predators in Shaping Prey Species: A Study of a Biological Ecosystem","authors":"Md. Mashih Ibn Yasin Adan,&nbsp;Md. Kamrujjaman,&nbsp;Ishrat Zahan","doi":"10.1002/mma.70737","DOIUrl":"https://doi.org/10.1002/mma.70737","url":null,"abstract":"<div>\u0000 \u0000 <p>This study analyzes critical threats to wildlife species' extinction, focusing on human activities, climatic challenges, and the Allee effect within ecological frameworks. We investigate the dynamics of two interacting reaction–diffusion models, particularly examining the harvesting of prey species proportional to their intrinsic growth rates. Our findings reveal significant depletion of prey populations, especially under intense predation pressure, leading to potential extinction. While coexistence between species is possible in the absence of harvesting, one species may drive the other to extinction under certain conditions. The analytical results are supported by numerical examples, emphasizing the need for sustainable harvesting practices to maintain ecological balance and prevent species endangerment.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13176-13200"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576137","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":"Representation of Solutions to Continuous and Discrete First-Order Linear Matrix Equations With Delay","authors":"Javad A. Asadzade,&nbsp;Nazim I. Mahmudov","doi":"10.1002/mma.70752","DOIUrl":"https://doi.org/10.1002/mma.70752","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we study continuous and discrete linear delay systems given respectively by \u0000\u0000 &lt;/p&gt;&lt;div&gt;&lt;span&gt;&lt;span&gt;&lt;!--FIGURE--&gt;&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;˙&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;mo&gt;+&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&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;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&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;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ξ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13412-13428"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565133","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":"Hölder Regularity of the Solutions of Fredholm Integral Equations on Upper Ahlfors Regular Sets","authors":"Massimo Lanza de Cristoforis,&nbsp;Manuel Norman","doi":"10.1002/mma.70725","DOIUrl":"https://doi.org/10.1002/mma.70725","url":null,"abstract":"<p>We extend to the context of metric measured spaces, with a measure that satisfies upper Ahlfors growth conditions, the validity of (generalized) Hölder continuity results for the solution of a Fredholm integral equation of the second kind. Here we note that upper Ahlfors growth conditions include also cases of nondoubling measures.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13361-13381"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70725","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565134","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":"Bifurcation Analysis of a Predator–Prey Model With Degenerate Diffusion and Multiple Allee Effects in Predators","authors":"Yafei Yang,&nbsp;Meng Fan","doi":"10.1002/mma.70728","DOIUrl":"https://doi.org/10.1002/mma.70728","url":null,"abstract":"<div>\u0000 \u0000 <p>Cooperative behaviors among individuals are prevalent in ecosystems and can trigger the Allee effect. To understand the combined effects of the cooperation-mediated Allee effect and mate limitation on population dynamics, a degenerate reaction–diffusion model is formulated by incorporating the component Allee effect and hunting cooperation. For the non-spatial scenario, the analytical results and numerical simulations show that the system exhibits rich dynamics such as cyclic phenomena, bistability, and Bogdanov–Takens bifurcation. For the reaction–diffusion model, sufficient conditions are derived for Turing instability and the existence of Hopf bifurcation, Turing bifurcation, and Turing–Hopf bifurcation are characterized. The key findings reveal that low-intensity component Allee effect and moderate cooperation can enhance the existence of predators and prey, while high-intensity component Allee effect and excessive cooperation may lead to the extinction of some population and spatiotemporal chaos. Meanwhile, degenerate diffusion can change the spatial structure of periodic solutions. Furthermore, the system exhibits complex critical transitions and spatiotemporal patterns near the Turing–Hopf bifurcation point, which provide valuable insights on species conservation and evasion of tipping points in complex ecosystems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13092-13122"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565145","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":"Qualitative Analysis of a Piecewise Immunosuppressive Infection Model With Nonlinear Threshold Policy Control","authors":"Xiong Zhang,&nbsp;Zhongyi Xiang","doi":"10.1002/mma.70716","DOIUrl":"https://doi.org/10.1002/mma.70716","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper examines a class of Filippov immunosuppressive infection models with nonlinear threshold functions to describe control strategies that are activated when viral suppression leads to the number of newly inactivated immune cells surpassing a specific threshold. It also discusses how sliding mode control and multi-stability can be utilized to modulate the therapeutic effect. The existence conditions for sliding segments, sliding dynamics, and several types of equilibria are derived, and theoretical and numerical analyses are performed on local bifurcations such as boundary-node bifurcation, boundary-focus bifurcation, boundary-saddle bifurcation, and boundary-saddle-node bifurcation. Findings suggest that the introduced model could exhibit multiple sliding segments, a situation linked to the nonlinear threshold function. Numerical global behavior analysis indicates that if the threshold for new inactivated immune cells is set excessively high or low, the threshold control strategy loses its effectiveness, potentially leading to an unbounded increase in viral load. Consequently, it is crucial to select an appropriate threshold level so that the number of newly inactivated immune cells is minimized or the fluctuation range is reduced, approaching the ideal attractor. Our exploration will provide evidence for treatments for AIDS and other diseases.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13216-13246"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576139","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}