Pub Date : 2026-10-01Epub Date: 2026-02-21DOI: 10.1016/j.cam.2026.117479
Ke-Yu Zhu , Gui-Xian Tian , Shu-Yu Cui
Given a graph G with vertex set and a graph H of order n2, the vertex complemented corona, denoted by , is the graph produced by copying H n1 times, with the ith copy of H corresponding to the vertex vi, and then adding edges between any vertex in V(G)∖{vi} and any vertex of the ith copy of H. The present article deals with quantum state transfer of vertex complemented coronas concerning signless Laplacian matrix. Our research investigates conditions in which signless Laplacian perfect state transfer exists or not on vertex complemented coronas. Additionally, we also provide some mild conditions for the class of graphs under consideration that allow signless Laplacian pretty good state transfer.
{"title":"Signless Laplacian state transfer on vertex complemented coronas","authors":"Ke-Yu Zhu , Gui-Xian Tian , Shu-Yu Cui","doi":"10.1016/j.cam.2026.117479","DOIUrl":"10.1016/j.cam.2026.117479","url":null,"abstract":"<div><div>Given a graph <em>G</em> with vertex set <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>{</mo><msub><mi>v</mi><mn>1</mn></msub><mo>,</mo><msub><mi>v</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>v</mi><msub><mi>n</mi><mn>1</mn></msub></msub><mo>}</mo></mrow></mrow></math></span> and a graph <em>H</em> of order <em>n</em><sub>2</sub>, the vertex complemented corona, denoted by <span><math><mrow><mi>G</mi><mover><mo>∘</mo><mo>˜</mo></mover><mi>H</mi></mrow></math></span>, is the graph produced by copying <em>H n</em><sub>1</sub> times, with the <em>i</em>th copy of <em>H</em> corresponding to the vertex <em>v<sub>i</sub></em>, and then adding edges between any vertex in <em>V</em>(<em>G</em>)∖{<em>v<sub>i</sub></em>} and any vertex of the <em>i</em>th copy of <em>H</em>. The present article deals with quantum state transfer of vertex complemented coronas concerning signless Laplacian matrix. Our research investigates conditions in which signless Laplacian perfect state transfer exists or not on vertex complemented coronas. Additionally, we also provide some mild conditions for the class of graphs under consideration that allow signless Laplacian pretty good state transfer.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117479"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386625","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}
Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117477
Omar El Ogri , Jaouad EL-Mekkaoui , Mohamed Benslimane , Amal Hjouji
Image analysis is a classic and commonplace task in the field of computer vision, widely applied over the past decade. Many existing methods in the literature are designed for signal and image analysis using the moments method show that most Dual Hahn moments applications are based on orthogonal polynomials of low order (n ≤ 128). However, the computation of high-order Dual Hahn polynomials remains highly constrained. Consequently, the primary objective of this study is to introduce two novel, stable, and efficient algorithms specifically designed for the computation of high-order Dual Hahn moments. The two algorithms rely on recently developed recurrence relations and the Gram-Schmidt Process (GSP), which take into account both the variable and order , removing the terms responsible for numerical fluctuations and excessive computation time, especially at high orders. The GSP is then commonly used to correct numerical instability during the calculation of high-order Discrete Orthogonal Dual Hahn Polynomials (DODHPs). These algorithms accelerate the implementation of DODHPs and ensure the numerical stability of orthogonal moments up to the final order through an analysis of the coefficient distribution within the polynomial matrix. An efficient method has also been developed to expedite the reconstruction time of large size 1D signals. To evaluate the proposed algorithms, we present several experimental tests on sets of signals and images. In this context, we evaluate our algorithms for compression and reconstruction of large 1D and 2D signals. Then, in recognition, we used our descriptor vector based on the proposed algorithms for image feature extraction, as well as the deep learning method DNN for image classification and prediction. These results demonstrate that the proposed algorithms for the speed and stability of large-size signals and 2D images outperform conventional methods and other types of existing moments.
{"title":"An efficient computational high-order Dual Hahn polynomials approach for reconstruction, compression, and recognition of large-size signals using machine learning","authors":"Omar El Ogri , Jaouad EL-Mekkaoui , Mohamed Benslimane , Amal Hjouji","doi":"10.1016/j.cam.2026.117477","DOIUrl":"10.1016/j.cam.2026.117477","url":null,"abstract":"<div><div>Image analysis is a classic and commonplace task in the field of computer vision, widely applied over the past decade. Many existing methods in the literature are designed for signal and image analysis using the moments method show that most Dual Hahn moments applications are based on orthogonal polynomials of low order (<em>n</em> ≤ 128). However, the computation of high-order Dual Hahn polynomials remains highly constrained. Consequently, the primary objective of this study is to introduce two novel, stable, and efficient algorithms specifically designed for the computation of high-order Dual Hahn moments. The two algorithms rely on recently developed recurrence relations and the Gram-Schmidt Process (GSP), which take into account both the variable <span><math><mi>s</mi></math></span> and order <span><math><mi>n</mi></math></span>, removing the terms responsible for numerical fluctuations and excessive computation time, especially at high orders. The GSP is then commonly used to correct numerical instability during the calculation of high-order Discrete Orthogonal Dual Hahn Polynomials (DODHPs). These algorithms accelerate the implementation of DODHPs and ensure the numerical stability of orthogonal moments up to the final order through an analysis of the coefficient distribution within the polynomial matrix. An efficient method has also been developed to expedite the reconstruction time of large size 1D signals. To evaluate the proposed algorithms, we present several experimental tests on sets of signals and images. In this context, we evaluate our algorithms for compression and reconstruction of large 1D and 2D signals. Then, in recognition, we used our descriptor vector based on the proposed algorithms for image feature extraction, as well as the deep learning method DNN for image classification and prediction. These results demonstrate that the proposed algorithms for the speed and stability of large-size signals and 2D images outperform conventional methods and other types of existing moments.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117477"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386628","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}
Pub Date : 2026-10-01Epub Date: 2026-02-24DOI: 10.1016/j.cam.2026.117469
Xiangli Li , Zhiling Wang , Binglan Li
In this paper, based on the excellent properties of Newton method, and the motivation of sufficient descent condition, we propose a new spectral hybrid conjugate gradient method. By using the secant line condition, the appropriate combination weight parameter is calculated. The spectral parameter is obtained under the rule of sufficient descent for search direction without any line search. Using the Wolfe line search, we prove the global convergence of the proposed method. Finally, numerical results show that the proposed method is effective.
{"title":"A improved spectral hybrid conjugate gradient method for unconstrained optimization","authors":"Xiangli Li , Zhiling Wang , Binglan Li","doi":"10.1016/j.cam.2026.117469","DOIUrl":"10.1016/j.cam.2026.117469","url":null,"abstract":"<div><div>In this paper, based on the excellent properties of Newton method, and the motivation of sufficient descent condition, we propose a new spectral hybrid conjugate gradient method. By using the secant line condition, the appropriate combination weight parameter is calculated. The spectral parameter is obtained under the rule of sufficient descent for search direction without any line search. Using the Wolfe line search, we prove the global convergence of the proposed method. Finally, numerical results show that the proposed method is effective.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117469"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386637","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}
Pub Date : 2026-10-01Epub Date: 2025-12-13DOI: 10.1016/j.nonrwa.2025.104574
Weidong Qin, Yunxian Dai, Doudou Lou
This paper investigates a delayed predator-prey model incorporating fear effects, prey refuge, Crowley-Martin type functional response, and cross-diffusion. First, we analyze the existence and stability of the positive equilibrium of the non-delay model. Then, we investigate the conditions for the occurrence of Turing instability in the delayed model. The amplitude equation is derived using the multiple-scale perturbation method, revealing the relationship between pattern selection and system parameters. Meanwhile, some numerical simulations are conducted to validate the accuracy of the theoretical analysis. The results demonstrate that varying control parameters can induce diverse patterns, including spots, stripes, and mixed patterns. Additionally, we find that the fear response delay affects the stabilization time of patterns, and as the delay increases, the patterns gradually become unstable. This study highlights the impact of the fear response delay on the stability and pattern formation in predator-prey systems, providing theoretical insights into the complexity of population dynamics.
{"title":"Pattern dynamics in a reaction-diffusion predator-prey model with fear response delay","authors":"Weidong Qin, Yunxian Dai, Doudou Lou","doi":"10.1016/j.nonrwa.2025.104574","DOIUrl":"10.1016/j.nonrwa.2025.104574","url":null,"abstract":"<div><div>This paper investigates a delayed predator-prey model incorporating fear effects, prey refuge, Crowley-Martin type functional response, and cross-diffusion. First, we analyze the existence and stability of the positive equilibrium of the non-delay model. Then, we investigate the conditions for the occurrence of Turing instability in the delayed model. The amplitude equation is derived using the multiple-scale perturbation method, revealing the relationship between pattern selection and system parameters. Meanwhile, some numerical simulations are conducted to validate the accuracy of the theoretical analysis. The results demonstrate that varying control parameters can induce diverse patterns, including spots, stripes, and mixed patterns. Additionally, we find that the fear response delay affects the stabilization time of patterns, and as the delay increases, the patterns gradually become unstable. This study highlights the impact of the fear response delay on the stability and pattern formation in predator-prey systems, providing theoretical insights into the complexity of population dynamics.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104574"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791665","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}
Pub Date : 2026-10-01Epub Date: 2026-02-27DOI: 10.1016/j.cam.2026.117531
Feng Xue
We discuss the possibility of reducing the alternating direction method of multipliers (ADMM) to a simple resolvent form, based on a degenerate proximal point algorithm (PPA). In particular, we reformulate ADMM as a standard PPA without correction step, where the variable metric helps to identify and remove the redundant variables. This approach can be a general routine for the degeneracy reduction of any splitting algorithms.
{"title":"On reducibility of ADMM based on degenerate proximal point analysis","authors":"Feng Xue","doi":"10.1016/j.cam.2026.117531","DOIUrl":"10.1016/j.cam.2026.117531","url":null,"abstract":"<div><div>We discuss the possibility of reducing the alternating direction method of multipliers (ADMM) to a simple resolvent form, based on a degenerate proximal point algorithm (PPA). In particular, we reformulate ADMM as a standard PPA without correction step, where the variable metric helps to identify and remove the redundant variables. This approach can be a general routine for the degeneracy reduction of any splitting algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117531"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386897","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}
Pub Date : 2026-10-01Epub Date: 2026-02-24DOI: 10.1016/j.cam.2026.117524
Yunbing Li , Wensheng Jia , Shuwen Xiang
Under the incentives of Nessah and Tian (2014) and Yang and Ju (2016), our study aims to investigate the existence and stability of strong equilibria in multi-leader-multi-follower games (MLMFGs) and multiobjective multi-leader-multi-follower games (MMLMFGs) under appropriate assumptions. Initially, we introduce the concepts of strong equilibria in both types of games, establishing their existence results by using Fan-Browder Theorem. Furthermore, we present a method for identifying strong equilibria in MLMFGs by providing a necessary and sufficient condition, and validate the approach through an illustrative example. In addition, we define a space for multiobjective multi-leader-multi-follower games that satisfies specific conditions, and then utilize Fort’s theorem to verify that the games within a dense residual set are essential relative to this space. Finally, we establish the existence of an essential component within the set of strong equilibrium solutions by examining the connectivity of minimal essential subset of the strong equilibrium solution set.
在Nessah and Tian（2014）和Yang and Ju（2016）的激励下，我们的研究旨在探讨在适当的假设下，多领导者-多追随者博弈（mlmfg）和多目标多领导者-多追随者博弈（mmlmfg）中强均衡的存在性和稳定性。首先，我们在这两类对策中引入了强均衡的概念，并利用Fan-Browder定理建立了它们的存在性结果。在此基础上，提出了一种识别mlmfg中强平衡点的方法，并给出了一个充要条件，并通过实例验证了该方法的有效性。此外，我们定义了满足特定条件的多目标多leader-多follower博弈空间，并利用Fort定理验证了密集残差集中的博弈相对于该空间是必要的。最后，通过检验强平衡解集的最小基本子集的连通性，证明了强平衡解集中存在一个基本分量。
{"title":"A new strong equilibrium of multi-leader-multi-follower games: Characterization and essential stability","authors":"Yunbing Li , Wensheng Jia , Shuwen Xiang","doi":"10.1016/j.cam.2026.117524","DOIUrl":"10.1016/j.cam.2026.117524","url":null,"abstract":"<div><div>Under the incentives of Nessah and Tian (2014) and Yang and Ju (2016), our study aims to investigate the existence and stability of strong equilibria in multi-leader-multi-follower games (MLMFGs) and multiobjective multi-leader-multi-follower games (MMLMFGs) under appropriate assumptions. Initially, we introduce the concepts of strong equilibria in both types of games, establishing their existence results by using Fan-Browder Theorem. Furthermore, we present a method for identifying strong equilibria in MLMFGs by providing a necessary and sufficient condition, and validate the approach through an illustrative example. In addition, we define a space for multiobjective multi-leader-multi-follower games that satisfies specific conditions, and then utilize Fort’s theorem to verify that the games within a dense residual set are essential relative to this space. Finally, we establish the existence of an essential component within the set of strong equilibrium solutions by examining the connectivity of minimal essential subset of the strong equilibrium solution set.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117524"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386996","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}
Pub Date : 2026-10-01Epub Date: 2026-01-31DOI: 10.1016/j.nonrwa.2026.104605
Stanislav Antontsev , Ivan Kuznetsov , Serik Aitzhanov
In the present paper, we study impulsive pseudo-parabolic equation with the nonlinear Robin boundary condition. In general, impulsive differential equations contain an approximation φn(t) of the Dirac delta function depending on . The support of φn(t) is the time interval [0, 1/n]. In order to pass to the limit as n → ∞, we apply rescaling and get a new initial-boundary value problem on an infinitesimal initial layer ϑ ∈ [0, 1]. In the limit, this problem allows us to calculate new initial data, which implies that there is a gap in the limit solution at . In the rest of the domain, outside of an infinitesimal initial layer, we apply shifting and obtain an initial boundary value problem in the limit without a singular source term, but with a new initial data.
{"title":"Impulsive pseudo-parabolic equation with nonlinear Robin boundary condition","authors":"Stanislav Antontsev , Ivan Kuznetsov , Serik Aitzhanov","doi":"10.1016/j.nonrwa.2026.104605","DOIUrl":"10.1016/j.nonrwa.2026.104605","url":null,"abstract":"<div><div>In the present paper, we study impulsive pseudo-parabolic equation with the nonlinear Robin boundary condition. In general, impulsive differential equations contain an approximation φ<sub><em>n</em></sub>(<em>t</em>) of the Dirac delta function depending on <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span>. The support of φ<sub><em>n</em></sub>(<em>t</em>) is the time interval [0, 1/<em>n</em>]. In order to pass to the limit as <em>n</em> → ∞, we apply rescaling <span><math><mrow><mi>ϑ</mi><mo>=</mo><mi>t</mi><mi>n</mi><mo>:</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mi>n</mi><mo>]</mo><mo>↦</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> and get a new initial-boundary value problem on an infinitesimal initial layer ϑ ∈ [0, 1]. In the limit, this problem allows us to calculate new initial data, which implies that there is a gap in the limit solution at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>. In the rest of the domain, outside of an infinitesimal initial layer, we apply shifting <span><math><mrow><mover><mrow><mi>t</mi></mrow><mo>˜</mo></mover><mo>:</mo><mo>=</mo><mi>t</mi><mo>−</mo><mfrac><mn>1</mn><mi>n</mi></mfrac></mrow></math></span> and obtain an initial boundary value problem in the limit without a singular source term, but with a new initial data.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104605"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188910","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}
Pub Date : 2026-10-01Epub Date: 2026-02-03DOI: 10.1016/j.nonrwa.2026.104614
Henan Wang , Ping Liu
This paper investigates a diffusive predator-prey model incorporating Allee effects in prey and a generalized Holling type IV functional response. The system features cross-diffusion terms to account for interspecific population pressures, significantly extending classical reaction-diffusion frameworks. We rigorously analyze the existence and nonexistence of nonconstant positive steady states using advanced mathematical methods, including the energy integral approach and Leray-Schauder degree theory. Key theoretical innovations establish that: (i) Nonconstant solutions are precluded when the criterion holds and diffusion coefficients (d1, d2) reside in a specific planar region; (ii) Conversely, sufficiently large cross-diffusion coefficient d4 guarantees the emergence of nonconstant steady states under explicit parameter constraints. These steady states correspond biologically to Turing patterns, indicative of spatially heterogeneous species coexistence. Extensive numerical simulations in 2D spatial domains confirm theoretical predictions, demonstrating pattern formation (e.g., spots, stripes) driven by cross-diffusion. The study provides novel analytical and computational insights into ecological pattern generation, with implications for spatial ecology and conservation strategies.
{"title":"Analysis of nonconstant steady states in a cross-diffusive predator-prey system with Allee effect and generalized Holling IV response","authors":"Henan Wang , Ping Liu","doi":"10.1016/j.nonrwa.2026.104614","DOIUrl":"10.1016/j.nonrwa.2026.104614","url":null,"abstract":"<div><div>This paper investigates a diffusive predator-prey model incorporating Allee effects in prey and a generalized Holling type IV functional response. The system features cross-diffusion terms to account for interspecific population pressures, significantly extending classical reaction-diffusion frameworks. We rigorously analyze the existence and nonexistence of nonconstant positive steady states using advanced mathematical methods, including the energy integral approach and Leray-Schauder degree theory. Key theoretical innovations establish that: (i) Nonconstant solutions are precluded when the criterion <span><math><mrow><msup><mi>d</mi><mi>σ</mi></msup><mrow><mo>(</mo><msub><mi>C</mi><mn>3</mn></msub><mo>+</mo><msub><mi>C</mi><mn>4</mn></msub><mo>)</mo></mrow><mo><</mo><mn>2</mn></mrow></math></span> holds and diffusion coefficients (<em>d</em><sub>1</sub>, <em>d</em><sub>2</sub>) reside in a specific planar region; (ii) Conversely, sufficiently large cross-diffusion coefficient <em>d</em><sub>4</sub> guarantees the emergence of nonconstant steady states under explicit parameter constraints. These steady states correspond biologically to Turing patterns, indicative of spatially heterogeneous species coexistence. Extensive numerical simulations in 2D spatial domains confirm theoretical predictions, demonstrating pattern formation (e.g., spots, stripes) driven by cross-diffusion. The study provides novel analytical and computational insights into ecological pattern generation, with implications for spatial ecology and conservation strategies.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104614"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188911","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}
Pub Date : 2026-10-01Epub Date: 2025-12-24DOI: 10.1016/j.nonrwa.2025.104584
Ifeanyi Sunday Onah
This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number Rv and establish conditions for the stability of the disease-free periodic solution. When Rv < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for Rv > 1, the infection is uniformly persistent and the system admits at least one positive T-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce Rv below one and interrupt sustained transmission.
{"title":"Seasonal dynamics and control of malaria: A non-autonomous model incorporating vaccination and drug resistance","authors":"Ifeanyi Sunday Onah","doi":"10.1016/j.nonrwa.2025.104584","DOIUrl":"10.1016/j.nonrwa.2025.104584","url":null,"abstract":"<div><div>This study develops and analyzes a seasonally forced malaria transmission model that incorporates vaccination, treatment, and the emergence of drug-resistant parasite strains. Using the periodic next-generation approach, we derive the vaccination-adjusted basic reproduction number <em>R<sub>v</sub></em> and establish conditions for the stability of the disease-free periodic solution. When <em>R<sub>v</sub></em> < 1, we show that malaria cannot persist and the disease-free state is globally asymptotically stable. Conversely, for <em>R<sub>v</sub></em> > 1, the infection is uniformly persistent and the system admits at least one positive <em>T</em>-periodic solution. A reduced autonomous version of the model reveals biologically interpretable thresholds for the dominance of either sensitive or resistant strains as well as coexistence scenarios. The model is calibrated using monthly malaria case data from Nigeria (2018–2024). The estimated reproduction number remains consistently above unity, indicating that malaria transmission is sustained under current intervention levels. Numerical simulations confirm these analytical results and illustrate the influence of vaccination coverage and drug resistance on long-term disease dynamics. Our findings highlight the need for strengthened intervention strategies to reduce <em>R<sub>v</sub></em> below one and interrupt sustained transmission.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104584"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841572","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}
Pub Date : 2026-10-01Epub Date: 2025-12-24DOI: 10.1016/j.nonrwa.2025.104581
L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon
In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree n, separated by the straight line . Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy , the system admits at most limit cycles. Furthermore, for the specific case , assuming d2 ≠ M2 and , we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.
{"title":"Limit cycles on rigid piecewise smooth dynamical systems governed by even polynomials","authors":"L.F. Gonçalves, A.C.T. Sánchez, D.J. Tonon","doi":"10.1016/j.nonrwa.2025.104581","DOIUrl":"10.1016/j.nonrwa.2025.104581","url":null,"abstract":"<div><div>In this work, we establish an upper bound for the number of crossing limit cycles in a class of piecewise smooth dynamical systems. The system is formed by a linear rigid center and a rigid center governed by a homogeneous polynomial of even degree <em>n</em>, separated by the straight line <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span>. Our results complement the work of [1], which addressed the odd-degree case. Specifically, we prove that if the parameters satisfy <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><msub><mi>M</mi><mn>2</mn></msub></mrow></math></span>, the system admits at most <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>2</mn></mrow></math></span> limit cycles. Furthermore, for the specific case <span><math><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow></math></span>, assuming <em>d</em><sub>2</sub> ≠ <em>M</em><sub>2</sub> and <span><math><mrow><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn></mrow></math></span>, we show that the system has at most one limit cycle, and this upper bound is attained. This study advances the analysis of this family of systems by covering the even-degree case under certain conditions on the affine transformation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104581"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841571","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}
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