We propose an energy-decreasing numerical scheme for the geodesic Willmore flow of closed curves on curved surfaces. This geometric flow characterizes the evolution of curves toward the minimization of the geodesic Willmore energy. Our main contributions are the derivation of novel evolution equations governing both the curve parameterization and geodesic curvature, the development of a stable fully discrete approximation combining the linear parametric finite elements in space with the implicit Euler in time, and a rigorous proof of discrete energy decay for the proposed scheme. The method effectively captures curve evolution on implicit surfaces. In addition, we generalize the energy-decreasing framework to the anisotropic geodesic Willmore flow and propose a BDF2 scheme. Through numerical experiments, we demonstrate the convergence and energy-decreasing property of the proposed approach, validating its effectiveness.
{"title":"Energy-decreasing parametric finite element method for geodesic Willmore flow","authors":"Cuiling Ma, Xufeng Xiao, Xiaoling Zhang, Xinlong Feng","doi":"10.1016/j.cnsns.2026.109783","DOIUrl":"10.1016/j.cnsns.2026.109783","url":null,"abstract":"<div><div>We propose an energy-decreasing numerical scheme for the geodesic Willmore flow of closed curves on curved surfaces. This geometric flow characterizes the evolution of curves toward the minimization of the geodesic Willmore energy. Our main contributions are the derivation of novel evolution equations governing both the curve parameterization and geodesic curvature, the development of a stable fully discrete approximation combining the linear parametric finite elements in space with the implicit Euler in time, and a rigorous proof of discrete energy decay for the proposed scheme. The method effectively captures curve evolution on implicit surfaces. In addition, we generalize the energy-decreasing framework to the anisotropic geodesic Willmore flow and propose a BDF2 scheme. Through numerical experiments, we demonstrate the convergence and energy-decreasing property of the proposed approach, validating its effectiveness.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109783"},"PeriodicalIF":3.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033538","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109670
Yanjiao Wang, Zhaogui Cai, Muqing Deng
Deep neural networks (DNNs) have the capability to describe complex nonlinear dynamics, which have aroused wide concerns. However, the existing parameter optimization methods in DNNs based on gradient suffer from the limitations of easily falling into local minima and the poor modeling results. To overcome these problems, this paper proposes a mini-batch gradient descent algorithm with dynamical moving window data and constructs a novel deep neural network architecture by using the simpler deep learning network instead of selecting weights through regulation and optimizing its parameters through the dynamical moving window based algorithm. The results of simulation experiments show that the proposed methods have better performance in accuracy and convergence rate compared with the existing methods for identifying nonlinear systems.
{"title":"A novel deep neural network with the dynamical moving window data for nonlinear system identification","authors":"Yanjiao Wang, Zhaogui Cai, Muqing Deng","doi":"10.1016/j.cnsns.2026.109670","DOIUrl":"10.1016/j.cnsns.2026.109670","url":null,"abstract":"<div><div>Deep neural networks (DNNs) have the capability to describe complex nonlinear dynamics, which have aroused wide concerns. However, the existing parameter optimization methods in DNNs based on gradient suffer from the limitations of easily falling into local minima and the poor modeling results. To overcome these problems, this paper proposes a mini-batch gradient descent algorithm with dynamical moving window data and constructs a novel deep neural network architecture by using the simpler deep learning network instead of selecting weights through regulation and optimizing its parameters through the dynamical moving window based algorithm. The results of simulation experiments show that the proposed methods have better performance in accuracy and convergence rate compared with the existing methods for identifying nonlinear systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109670"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033543","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109746
Xinlong Xu , Xia Huang , Qingyu Shi , Zhen Wang
This paper studies the synchronization problem of a class of unknown nonlinear systems. In response to the challenges in controller design resulting from unknown models, a lazy-learning-based Koopman model predictive control (LL-KMPC) strategy is proposed. The distinctiveness of the proposed control strategy is twofold: (i) exploitation of the global linearization property of the Koopman operator, enabling linear-control methods for synchronization control of unknown nonlinear systems; and (ii) integration of lazy learning (LL), which substantially reduces model mismatch in Koopman-based modeling. Moreover, theoretical results prove that the synchronization error is bounded under the proposed control strategy. Finally, two examples are provided to verify the effectiveness of the proposed control strategy. The experimental results demonstrate that the introduction of the LL technique can effectively improve the modeling performance, and compared to the model-free adaptive control (MFAC) and the model-free adaptive predictive control (MFAPC) approaches, the LL-KMPC strategy exhibits a faster convergence rate and a smaller synchronization error.
{"title":"Lazy-learning-based Koopman model predictive control for synchronization of unknown nonlinear systems","authors":"Xinlong Xu , Xia Huang , Qingyu Shi , Zhen Wang","doi":"10.1016/j.cnsns.2026.109746","DOIUrl":"10.1016/j.cnsns.2026.109746","url":null,"abstract":"<div><div>This paper studies the synchronization problem of a class of unknown nonlinear systems. In response to the challenges in controller design resulting from unknown models, a lazy-learning-based Koopman model predictive control (LL-KMPC) strategy is proposed. The distinctiveness of the proposed control strategy is twofold: (i) exploitation of the global linearization property of the Koopman operator, enabling linear-control methods for synchronization control of unknown nonlinear systems; and (ii) integration of lazy learning (LL), which substantially reduces model mismatch in Koopman-based modeling. Moreover, theoretical results prove that the synchronization error is bounded under the proposed control strategy. Finally, two examples are provided to verify the effectiveness of the proposed control strategy. The experimental results demonstrate that the introduction of the LL technique can effectively improve the modeling performance, and compared to the model-free adaptive control (MFAC) and the model-free adaptive predictive control (MFAPC) approaches, the LL-KMPC strategy exhibits a faster convergence rate and a smaller synchronization error.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109746"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033544","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109777
Pham Ky Anh , Ngo Thi Thuong , Nguyen The Vinh
In this paper, by combining the inertial technique and subgradient extragradient method with a new strategy of stepsize selection, we propose a novel extragradient-type method to solve pseudomonotone equilibrium problems in real Hilbert spaces. Our method is designed such that the stepsize sequence is increasing after a finite number of iterations. This distinguishes our method from most other extragradient-type methods for equilibrium problems. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our methods on the Nash-Cournot oligopolistic equilibrium models of electricity markets. The reported numerical results demonstrate the efficiency of the proposed method.
{"title":"Novel subgradient extragradient methods for equilibrium problems in Hilbert spaces","authors":"Pham Ky Anh , Ngo Thi Thuong , Nguyen The Vinh","doi":"10.1016/j.cnsns.2026.109777","DOIUrl":"10.1016/j.cnsns.2026.109777","url":null,"abstract":"<div><div>In this paper, by combining the inertial technique and subgradient extragradient method with a new strategy of stepsize selection, we propose a novel extragradient-type method to solve pseudomonotone equilibrium problems in real Hilbert spaces. Our method is designed such that the stepsize sequence is increasing after a finite number of iterations. This distinguishes our method from most other extragradient-type methods for equilibrium problems. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our methods on the Nash-Cournot oligopolistic equilibrium models of electricity markets. The reported numerical results demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109777"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033542","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109750
Alessandro Ramponi, Sergio Scarlatti
Inspired by the classical Vasicek approach to credit risk, we propose an extended model for portfolios composed of green and brown loans, widening the Asymptotic Single Risk Factor framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, collateralized default obligations pricing, and empirical analysis of green loan portfolios.
{"title":"Credit risk for large portfolios of green and brown loans: Extending the ASRF model","authors":"Alessandro Ramponi, Sergio Scarlatti","doi":"10.1016/j.cnsns.2026.109750","DOIUrl":"10.1016/j.cnsns.2026.109750","url":null,"abstract":"<div><div>Inspired by the classical Vasicek approach to credit risk, we propose an extended model for portfolios composed of green and brown loans, widening the Asymptotic Single Risk Factor framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, collateralized default obligations pricing, and empirical analysis of green loan portfolios.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109750"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033546","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109737
Peter E. Kloeden , Doan Thai Son , Hoang The Tuan
The asymptotic behaviour of a class of dissipative Caputo fractional differential equations with two indices is investigated. Using Lyapunov methods and a comparison principle, results on ultimate boundedness and Mittag-Leffler stability are obtained for these systems. Two examples illustrate these results.
{"title":"Lyapunov methods for dissipative Caputo fractional differential equations with two indices","authors":"Peter E. Kloeden , Doan Thai Son , Hoang The Tuan","doi":"10.1016/j.cnsns.2026.109737","DOIUrl":"10.1016/j.cnsns.2026.109737","url":null,"abstract":"<div><div>The asymptotic behaviour of a class of dissipative Caputo fractional differential equations with two indices is investigated. Using Lyapunov methods and a comparison principle, results on ultimate boundedness and Mittag-Leffler stability are obtained for these systems. Two examples illustrate these results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109737"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033940","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109778
Liangliang Sun, Zhaoqi Zhang
In this paper, we study a backward problem in a system controlled by two coupled time-fractional diffusion equations from the final measurement data. Firstly, we prove the well-posedness of the state problem by introducing the Riemann-Liouville weak formulation, and give some regularity results of the solution to the state problem by employing the properties of the Mittag-Leffler function. In order to solve this inverse problem, we then transform it into a least square optimization problem. Subsequently, we establish the existence of the minimizer and also prove its uniqueness and a stability estimates with respect to the input data. Finally, we provide some numerical results for the optimal control problem using the Landweber iterative method.
{"title":"Backward problem in a coupled time-fractional reaction diffusion system by optimization method","authors":"Liangliang Sun, Zhaoqi Zhang","doi":"10.1016/j.cnsns.2026.109778","DOIUrl":"10.1016/j.cnsns.2026.109778","url":null,"abstract":"<div><div>In this paper, we study a backward problem in a system controlled by two coupled time-fractional diffusion equations from the final measurement data. Firstly, we prove the well-posedness of the state problem by introducing the Riemann-Liouville weak formulation, and give some regularity results of the solution to the state problem by employing the properties of the Mittag-Leffler function. In order to solve this inverse problem, we then transform it into a least square optimization problem. Subsequently, we establish the existence of the minimizer and also prove its uniqueness and a stability estimates with respect to the input data. Finally, we provide some numerical results for the optimal control problem using the Landweber iterative method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109778"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033547","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109767
Yaojia Zhang , Tao Chen , Stanislaw Migórski
This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.
{"title":"Viscoelastic surfactant flowback model with rod-like micelle leading to differential variational-hemivariational inequality","authors":"Yaojia Zhang , Tao Chen , Stanislaw Migórski","doi":"10.1016/j.cnsns.2026.109767","DOIUrl":"10.1016/j.cnsns.2026.109767","url":null,"abstract":"<div><div>This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109767"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033540","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109775
Yudong Zhou, Qinghui Zhang
Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for L2 relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.
{"title":"Extreme learning machines with decaying penalties for nonlinear partial differential equations","authors":"Yudong Zhou, Qinghui Zhang","doi":"10.1016/j.cnsns.2026.109775","DOIUrl":"10.1016/j.cnsns.2026.109775","url":null,"abstract":"<div><div>Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for <em>L</em><sup>2</sup> relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109775"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033905","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 : 2026-01-22DOI: 10.1016/j.cnsns.2026.109760
Xiumei Deng , Qihua Huang , Hai-Yang Jin
We develop a reaction-diffusion-taxis model to investigate the dynamic interactions between a toxicant and a predator-prey system within a contaminated aquatic ecosystem. The model includes taxis terms induced by the toxicant to capture the evasive movement of individuals as they seek to avoid exposure to the toxicant. We establish the global well-posedness of solutions for the reaction-diffusion-taxis system. We prove the global asymptotic stability of spatially uniform steady states. Through linear stability analysis, we derive sufficient conditions for the destabilization of these uniform steady states. Numerically, we explore the influence of key toxicant-related parameters—such as toxicant input rate, toxicant-taxis intensity, and species susceptibility to toxicants—on the persistence and spatial distribution of prey and predator populations. Our results demonstrate that: (i) High-intensity toxicant-taxis can induce spatial segregation and aggregation patterns between the toxicant and populations; (ii) when predators are more susceptible to toxicants than their prey, a moderate increase in toxicant concentration may, counterintuitively, enhance prey persistence; and (iii) spatially heterogeneous toxicant inputs can promote species persistence, thereby supporting ecosystem biodiversity.
{"title":"A reaction-diffusion-taxis model for toxicant-predator-prey interaction dynamics","authors":"Xiumei Deng , Qihua Huang , Hai-Yang Jin","doi":"10.1016/j.cnsns.2026.109760","DOIUrl":"10.1016/j.cnsns.2026.109760","url":null,"abstract":"<div><div>We develop a reaction-diffusion-taxis model to investigate the dynamic interactions between a toxicant and a predator-prey system within a contaminated aquatic ecosystem. The model includes taxis terms induced by the toxicant to capture the evasive movement of individuals as they seek to avoid exposure to the toxicant. We establish the global well-posedness of solutions for the reaction-diffusion-taxis system. We prove the global asymptotic stability of spatially uniform steady states. Through linear stability analysis, we derive sufficient conditions for the destabilization of these uniform steady states. Numerically, we explore the influence of key toxicant-related parameters—such as toxicant input rate, toxicant-taxis intensity, and species susceptibility to toxicants—on the persistence and spatial distribution of prey and predator populations. Our results demonstrate that: (i) High-intensity toxicant-taxis can induce spatial segregation and aggregation patterns between the toxicant and populations; (ii) when predators are more susceptible to toxicants than their prey, a moderate increase in toxicant concentration may, counterintuitively, enhance prey persistence; and (iii) spatially heterogeneous toxicant inputs can promote species persistence, thereby supporting ecosystem biodiversity.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109760"},"PeriodicalIF":3.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033904","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}
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