Pub Date : 2026-12-01Epub Date: 2026-02-04DOI: 10.1016/j.nonrwa.2026.104617
Yijie Zha , Xun Cao
This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if , the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if , the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.
{"title":"Threshold dynamics of a reaction-diffusion-advection schistosomiasis model with seasonality","authors":"Yijie Zha , Xun Cao","doi":"10.1016/j.nonrwa.2026.104617","DOIUrl":"10.1016/j.nonrwa.2026.104617","url":null,"abstract":"<div><div>This paper proposes a reaction-diffusion-advection schistosomiasis model with seasonality based on the life cycle of schistosomiasis (humans, eggs, snails, and cercariae). Using the next generation operator theory, we define the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> that characterizes the transmission potential of schistosomiasis, and further reveal the threshold dynamics of the system through the monotone dynamical system theory. Specifically, if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, the disease-free periodic solution is globally asymptotically stable, meaning that schistosomiasis will die out; if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span>, the system admits a unique positive periodic solution that is globally asymptotically stable, indicating that the disease will break out. Numerically, we use data from Ourinhos, Brazil, to analyze the impact of diffusion rates, spatial heterogeneity, advection rates, and seasonality on the transmission of schistosomiasis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104617"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116723","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 : 2026-12-01Epub Date: 2026-02-04DOI: 10.1016/j.nonrwa.2026.104615
Xiuwen Li , Zhenhai Liu , Jing Zhao
Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (m-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.
{"title":"Well-posedness results and global attractors for a generalized coupled dynamical system","authors":"Xiuwen Li , Zhenhai Liu , Jing Zhao","doi":"10.1016/j.nonrwa.2026.104615","DOIUrl":"10.1016/j.nonrwa.2026.104615","url":null,"abstract":"<div><div>Our present paper investigates theoretical results concerning the well-posedness and global attractor of a novel class of generalized coupling dynamical systems (GCDSs). The system comprises an abstract nonlinear differential inclusion with a history-dependent (h.d.) operator and a generalized variational-hemivariational inequality (GVHVI) with two h.d. operators, formulated within Banach spaces. Our study unfolds in four key aspects. First, we introduce and establish the well-posedness results of the GVHVI by employing the surjectivity theorem for multivalued mappings and techniques from nonlinear functional analysis. Second, we consider and discuss the existence of solutions to the GCDSs by using fixed-point theory under some suitable assumptions. Third, we explore and derive the existence of global attractors for the multivalued semiflow (<em>m</em>-semiflow) described by the GCDSs under some sufficient conditions. Finally, we present an application to a coupled problem, demonstrating the applicability of our theoretical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"92 ","pages":"Article 104615"},"PeriodicalIF":1.8,"publicationDate":"2026-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146116724","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: 2026-01-07DOI: 10.1016/j.nonrwa.2025.104600
Andaluzia Matei
In the present paper we draw attention to a strongly coupled nonlinear system consisting of two variational inequalities. Such a system can arise from weak formulations of contact models with implicit material laws governed by non additively-separable g-bipotentials. A multi-contact model applying to an implicit standard material illustrates the theory. Firstly, we deliver abstract results. Then, we apply the abstract results to the well-posedness of the multi-contact model under consideration.
{"title":"Nonlinear variational systems related to contact models with implicit material laws","authors":"Andaluzia Matei","doi":"10.1016/j.nonrwa.2025.104600","DOIUrl":"10.1016/j.nonrwa.2025.104600","url":null,"abstract":"<div><div>In the present paper we draw attention to a strongly coupled nonlinear system consisting of two variational inequalities. Such a system can arise from weak formulations of contact models with implicit material laws governed by non additively-separable g-bipotentials. A multi-contact model applying to an implicit standard material illustrates the theory. Firstly, we deliver abstract results. Then, we apply the abstract results to the well-posedness of the multi-contact model under consideration.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104600"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926981","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: 2026-02-14DOI: 10.1016/j.cam.2026.117454
Guo Qiu Wang , Wei Liang
Building upon the concept of discretely orthogonal bases, this paper develops a generalized interpolation framework, with the classical Lagrange interpolation method serving as a special case. Specifically, for an arbitrary number of specific non-equidistant interpolation nodes, this paper constructs corresponding discretely orthogonal polynomial bases, whose associated orthogonal matrices coincide with the well-known Discrete Cosine Transforms (DCTs). Using these polynomial bases, we show that when interpolation nodes are chosen as extended Chebyshev nodes, the interpolation of continuous functions converge in the square-integrable sense. Furthermore, we prove that the resulting interpolation functions based on extended Chebyshev nodes exhibit uniform convergence in the Hölder continuity class. These results not only provide a rigorous theoretical foundation for polynomial-based signal representation in digital conditioning of sensors, but also suggest a viable candidate for spectral-type approach for numerical schemes for partial differential equations (PDEs).
{"title":"Non-orthogonal interpolation on closed interval and convergence","authors":"Guo Qiu Wang , Wei Liang","doi":"10.1016/j.cam.2026.117454","DOIUrl":"10.1016/j.cam.2026.117454","url":null,"abstract":"<div><div>Building upon the concept of discretely orthogonal bases, this paper develops a generalized interpolation framework, with the classical Lagrange interpolation method serving as a special case. Specifically, for an arbitrary number of specific non-equidistant interpolation nodes, this paper constructs corresponding discretely orthogonal polynomial bases, whose associated orthogonal matrices coincide with the well-known Discrete Cosine Transforms (DCTs). Using these polynomial bases, we show that when interpolation nodes are chosen as extended Chebyshev nodes, the interpolation of continuous functions converge in the square-integrable sense. Furthermore, we prove that the resulting interpolation functions based on extended Chebyshev nodes exhibit uniform convergence in the Hölder continuity class. These results not only provide a rigorous theoretical foundation for polynomial-based signal representation in digital conditioning of sensors, but also suggest a viable candidate for spectral-type approach for numerical schemes for partial differential equations (PDEs).</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117454"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387183","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: 2026-02-10DOI: 10.1016/j.cam.2026.117418
Dean Chou , Ifrah Iqbal , Yasser Alrashedi , Theyab Alrashdi , Hamood Ur Rehman
In this research, we examine the equal-width equation, a basic model for one-dimensional wave propagation in nonlinear fluid dynamics. Using the Kudryashov method, we obtain explicit soliton solutions that reflect the equation’s inherent nonlinear nature, modeling different hydrodynamic phenomena like shallow water waves and internal solitons. The solutions are graphically represented using three-dimensional (3D), contour, density, and two-dimensional (2D) plots to gain further insight into wave evolution. To confirm the analytical solutions, we apply the differential transform method (DTM) for numerical simulations, allowing for comparative analysis between theoretical solitons and their discrete approximations. In addition, stability and modulation instability analyses are conducted to determine the robustness of these wave structures under small perturbations, important for understanding turbulence and energy dissipation in fluids. Furthermore, we perform a bifurcation analysis through the building of phase portraits and vector fields, uncovering complex dynamical behaviors like periodic and chaotic motion in nonlinear fluid systems. In order to expand our investigation, we add a periodic perturbation to investigate chaotic wave interactions, represented through phase space trajectories and time series plots. The perturbed system presents a perturbation with elements of intensity δ and frequency ϕ, enabling us to study how small periodic perturbations influence the dynamical behavior and stability of the nonlinear wave solutions. Finally, we investigate multistability and carry out sensitivity analysis, evaluating how initial conditions affect solution trajectories in a fluid system. Our results are helping toward a deeper understanding of nonlinear wave mechanics and their repercussions in fluid physics. This work addresses the lack of a unified framework by combining exact soliton solutions, numerical validation, and nonlinear dynamical analysis for the equal-width equation.
{"title":"Bifurcation, chaotic behaviour, multistability and sensitivity analysis: Exact and numerical analysis of nonlinear dispersive wave equation","authors":"Dean Chou , Ifrah Iqbal , Yasser Alrashedi , Theyab Alrashdi , Hamood Ur Rehman","doi":"10.1016/j.cam.2026.117418","DOIUrl":"10.1016/j.cam.2026.117418","url":null,"abstract":"<div><div>In this research, we examine the equal-width equation, a basic model for one-dimensional wave propagation in nonlinear fluid dynamics. Using the Kudryashov method, we obtain explicit soliton solutions that reflect the equation’s inherent nonlinear nature, modeling different hydrodynamic phenomena like shallow water waves and internal solitons. The solutions are graphically represented using three-dimensional (3D), contour, density, and two-dimensional (2D) plots to gain further insight into wave evolution. To confirm the analytical solutions, we apply the differential transform method (DTM) for numerical simulations, allowing for comparative analysis between theoretical solitons and their discrete approximations. In addition, stability and modulation instability analyses are conducted to determine the robustness of these wave structures under small perturbations, important for understanding turbulence and energy dissipation in fluids. Furthermore, we perform a bifurcation analysis through the building of phase portraits and vector fields, uncovering complex dynamical behaviors like periodic and chaotic motion in nonlinear fluid systems. In order to expand our investigation, we add a periodic perturbation to investigate chaotic wave interactions, represented through phase space trajectories and time series plots. The perturbed system presents a perturbation with elements of intensity <em>δ</em> and frequency <em>ϕ</em>, enabling us to study how small periodic perturbations influence the dynamical behavior and stability of the nonlinear wave solutions. Finally, we investigate multistability and carry out sensitivity analysis, evaluating how initial conditions affect solution trajectories in a fluid system. Our results are helping toward a deeper understanding of nonlinear wave mechanics and their repercussions in fluid physics. This work addresses the lack of a unified framework by combining exact soliton solutions, numerical validation, and nonlinear dynamical analysis for the equal-width equation.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117418"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387184","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}
This paper presents a C-FISTA-type proximal point algorithm for solving strongly quasiconvex pseudomonotone equilibrium problems. Our proposed method consists of two momentum terms, a correction term, and the proximal point algorithm. We establish the convergence of our proposed method under standard assumptions. Furthermore, we obtain the sublinear and linear convergence rates of our proposed method. Finally, we present a numerical test for solving equilibrium problems to illustrate the effectiveness and versatility of our proposed method.
{"title":"A C-FISTA-type proximal point algorithm for strongly quasiconvex pseudomonotone equilibrium problems","authors":"Grace Nnennaya Ogwo , Chinedu Izuchukwu , Yekini Shehu","doi":"10.1016/j.cam.2026.117504","DOIUrl":"10.1016/j.cam.2026.117504","url":null,"abstract":"<div><div>This paper presents a C-FISTA-type proximal point algorithm for solving strongly quasiconvex pseudomonotone equilibrium problems. Our proposed method consists of two momentum terms, a correction term, and the proximal point algorithm. We establish the convergence of our proposed method under standard assumptions. Furthermore, we obtain the sublinear and linear convergence rates of our proposed method. Finally, we present a numerical test for solving equilibrium problems to illustrate the effectiveness and versatility of our proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117504"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386988","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.2026.117476
Na-Na Wang , Ji-Cheng Li
In this paper, a class of product-type (PT) preconditioners for generalized saddle point problems recently proposed in [N. Wang, J. Li, A class of preconditioners based on symmetric-triangular decomposition and matrix splitting for generalized saddle point problems, IMA J. Numer. Anal., (2023) 43, 2998–3025] are extended to solve the double saddle point problems arising from the modeling of liquid crystal directors. By combining augmented Lagrangian (AL) technique, two specific block PT preconditioners are developed, which are applied appropriately with the efficient conjugate gradient (CG) and conjugate residual (CR) methods although neither the preconditioners nor the double saddle point systems are symmetric positive definite (SPD). This is the biggest advantage and novelty of the proposed preconditioners. The proposed preconditioned CG (PCG) and preconditioned CR (PCR) methods actually belong to the categories of nonstandard inner product CG and nonstandard inner product CR methods, respectively. Moreover, the PCG and PCR algorithms and their convergence theorems are given. Theoretical and experimental analysis shows that the spectra of the preconditioned matrices are contained within real and positive intervals which are very sharp if the involved parameters are chosen appropriately. In addition, the practically useful values for parameters are easy to obtain. Numerical experiments are presented to illustrate the rapidity, effectiveness and numerical stability of the proposed preconditioners and show the advantages of the proposed preconditioners over the existing state-of-the-art preconditioners for double saddle point problems.
{"title":"Two block product-type preconditioners for double saddle point problems","authors":"Na-Na Wang , Ji-Cheng Li","doi":"10.1016/j.cam.2026.117476","DOIUrl":"10.1016/j.cam.2026.117476","url":null,"abstract":"<div><div>In this paper, a class of product-type (PT) preconditioners for generalized saddle point problems recently proposed in [N. Wang, J. Li, A class of preconditioners based on symmetric-triangular decomposition and matrix splitting for generalized saddle point problems, IMA J. Numer. Anal., (2023) 43, 2998–3025] are extended to solve the double saddle point problems arising from the modeling of liquid crystal directors. By combining augmented Lagrangian (AL) technique, two specific block PT preconditioners are developed, which are applied appropriately with the efficient conjugate gradient (CG) and conjugate residual (CR) methods although neither the preconditioners nor the double saddle point systems are symmetric positive definite (SPD). This is the biggest advantage and novelty of the proposed preconditioners. The proposed preconditioned CG (PCG) and preconditioned CR (PCR) methods actually belong to the categories of nonstandard inner product CG and nonstandard inner product CR methods, respectively. Moreover, the PCG and PCR algorithms and their convergence theorems are given. Theoretical and experimental analysis shows that the spectra of the preconditioned matrices are contained within real and positive intervals which are very sharp if the involved parameters are chosen appropriately. In addition, the practically useful values for parameters are easy to obtain. Numerical experiments are presented to illustrate the rapidity, effectiveness and numerical stability of the proposed preconditioners and show the advantages of the proposed preconditioners over the existing state-of-the-art preconditioners for double saddle point problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117476"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386993","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: 2026-02-26DOI: 10.1016/j.cam.2026.117473
F. Arenas , R. Pérez , M. Gonzalez-Lima , C.A. Arias
In this paper we present a centered Newton type algorithm for solving the nonlinear complementarity problem by a reformulation of the problem as a nonlinear system of equations with nonnegativity constraints. The proposed algorithm considers centered Newton directions projected over the feasible set in order to maintain iterate feasibility. We present theoretical and numerical results for the proposal.
{"title":"A centered Newton method for nonlinear complementarity problem","authors":"F. Arenas , R. Pérez , M. Gonzalez-Lima , C.A. Arias","doi":"10.1016/j.cam.2026.117473","DOIUrl":"10.1016/j.cam.2026.117473","url":null,"abstract":"<div><div>In this paper we present a centered Newton type algorithm for solving the nonlinear complementarity problem by a reformulation of the problem as a nonlinear system of equations with nonnegativity constraints. The proposed algorithm considers centered Newton directions projected over the feasible set in order to maintain iterate feasibility. We present theoretical and numerical results for the proposal.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117473"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386997","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: 2025-12-18DOI: 10.1016/j.nonrwa.2025.104562
Lin Zhao, Yini Liu
In this paper, we focus on a Zika virus model with diffusion and constant recruitment and analyze the existence and non-existence of traveling wave solutions of the model, which are determined by the basic reproduction number R0 and the minimal wave speed c*. Precisely speaking, if R0 > 1, then there exists a minimal wave speed c* > 0 such that the model admits traveling wave solutions with the wave speed c ≥ c*, and there are no non-trivial traveling wave solutions of this model with 0 < c < c*. If R0 ≤ 1, we prove that there are no non-trivial traveling wave solutions of the model. Finally, numerical simulations are carried out to verify and demonstrate some of the conclusions obtained in this study.
本文研究了一种具有扩散和不断招募的Zika病毒模型，分析了该模型的行波解的存在性和不存在性，其存在性由基本繁殖数R0和最小波速c*决定。准确地讲,如果R0 祝辞 1,那么存在一个最小波速c * 祝辞 0这样的模型承认行波解和波速c ≥ c *,并且没有不平凡的这个模型的行波解与0 & lt; c & lt; c *。当R0 ≤ 1时，我们证明了模型不存在非平凡行波解。最后，通过数值模拟验证和论证了本文的部分结论。
{"title":"Propagation dynamics of a Zika virus model with diffusion and constant recruitment","authors":"Lin Zhao, Yini Liu","doi":"10.1016/j.nonrwa.2025.104562","DOIUrl":"10.1016/j.nonrwa.2025.104562","url":null,"abstract":"<div><div>In this paper, we focus on a Zika virus model with diffusion and constant recruitment and analyze the existence and non-existence of traveling wave solutions of the model, which are determined by the basic reproduction number <em>R</em><sub>0</sub> and the minimal wave speed <em>c</em>*. Precisely speaking, if <em>R</em><sub>0</sub> > 1, then there exists a minimal wave speed <em>c</em>* > 0 such that the model admits traveling wave solutions with the wave speed <em>c</em> ≥ <em>c</em>*, and there are no non-trivial traveling wave solutions of this model with 0 < <em>c</em> < <em>c</em>*. If <em>R</em><sub>0</sub> ≤ 1, we prove that there are no non-trivial traveling wave solutions of the model. Finally, numerical simulations are carried out to verify and demonstrate some of the conclusions obtained in this study.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104562"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791715","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: 2025-12-15DOI: 10.1016/j.nonrwa.2025.104561
Xinshan Dong , Ben Niu , Lin Wang
We investigate a diffusive Rosenzweig-MacArthur system that includes nonlocal prey competition and prey-taxis under Neumann boundary conditions. Initially, we establish the global existence and boundedness of solutions for arbitrary spatial dimensions and small prey-taxis sensitivity coefficient. Subsequently, we analyze the local stability of the constant steady-state solution. Using the Lyapunov-Schmidt reduction method, we explore several bifurcations near the positive constant steady-state: steady-state bifurcation, Hopf bifurcation, and their interaction. Finally, numerical simulations are performed to validate our theoretical findings and illustrate complex spatiotemporal patterns. By selecting appropriate parameters and initial conditions, our simulations reveal the coexistence of a pair of stable spatially nonhomogeneous steady-states and stable spatially homogeneous periodic solutions, which indicates the system exhibits tristability, that is, the coexistence of three distinct stable states. Moreover, our results demonstrate that transient patterns transition from spatially nonhomogeneous periodic solutions to spatially nonhomogeneous steady-state and spatially homogeneous periodic solutions.
{"title":"Spatiotemporal patterns induced by nonlocal prey competition and prey-taxis in a diffusive Rosenzweig-MacArthur system","authors":"Xinshan Dong , Ben Niu , Lin Wang","doi":"10.1016/j.nonrwa.2025.104561","DOIUrl":"10.1016/j.nonrwa.2025.104561","url":null,"abstract":"<div><div>We investigate a diffusive Rosenzweig-MacArthur system that includes nonlocal prey competition and prey-taxis under Neumann boundary conditions. Initially, we establish the global existence and boundedness of solutions for arbitrary spatial dimensions and small prey-taxis sensitivity coefficient. Subsequently, we analyze the local stability of the constant steady-state solution. Using the Lyapunov-Schmidt reduction method, we explore several bifurcations near the positive constant steady-state: steady-state bifurcation, Hopf bifurcation, and their interaction. Finally, numerical simulations are performed to validate our theoretical findings and illustrate complex spatiotemporal patterns. By selecting appropriate parameters and initial conditions, our simulations reveal the coexistence of a pair of stable spatially nonhomogeneous steady-states and stable spatially homogeneous periodic solutions, which indicates the system exhibits tristability, that is, the coexistence of three distinct stable states. Moreover, our results demonstrate that transient patterns transition from spatially nonhomogeneous periodic solutions to spatially nonhomogeneous steady-state and spatially homogeneous periodic solutions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"91 ","pages":"Article 104561"},"PeriodicalIF":1.8,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791662","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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