Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"The delayed reaction-diffusion Filippov system with threshold control: Modeling and analysis of plateau pika-vegetation dynamics","authors":"Jianping Lv, Jing Li","doi":"10.1016/j.cnsns.2025.109366","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109366","url":null,"abstract":"Plateau pika (Ochotona curzoniae) plays dual ecological roles: enhancing biodiversity at moderate population densities, but driving severe grassland degradation during population outbreaks. To capture these phenomena, we develop delayed reaction-diffusion Filippov systems incorporating Holling-III functional response, maturation time delays, prey-taxis behavior, and threshold-based control strategies. Two types of threshold controls are considered: a single-threshold model, where intervention is triggered only when vegetation density drops below a threshold <mml:math altimg=\"si1.svg\"><mml:mi>T</mml:mi></mml:math>; and a dual-threshold model, which introduces an additional pika density threshold <mml:math altimg=\"si15.svg\"><mml:mrow><mml:mi>H</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math> to enable preventive control. We establish the well-posedness of solutions, analyze equilibrium stability and Hopf bifurcations, and characterize sliding mode dynamics via Filippov’s convex method, thereby identifying pseudoequilibria and their stability conditions. Numerical simulations demonstrate that the dual-threshold strategy substantially outperforms the single-threshold approach by preventing extreme pika aggregation, maintaining more uniform vegetation distribution, and reducing grassland degradation. This dual-threshold mechanism highlights a paradigm shift from reactive to proactive ecological management. Our findings provide theoretical support for sustainable grassland management on the Tibetan Plateau.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"18 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261914","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}

{"title":"Subspace method based on neural networks for solving the partial differential equation in weak form","authors":"Pengyuan Liu, Zhaodong Xu, Zhiqiang Sheng","doi":"10.1016/j.cnsns.2025.109367","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109367","url":null,"abstract":"In this paper, we propose a subspace method based on neural networks for solving the partial differential equations (PDEs) in weak form. The method uses neural network-based functions as basis functions to span a subspace, within which an approximate solution is sought. The related algorithms are developed to address both linear and nonlinear PDEs with various boundary conditions in weak form. To improve the approximation capabilities of the subspace, multiple training strategies are employed. Numerical experiments demonstrate that the proposed method achieves high accuracy with minimal computational cost, requiring only 100 to 2,000 training epochs in most cases. The method offers significant advantages in both accuracy and computational efficiency. The codes and data associated with this work are openly available at <ce:inter-ref xlink:href=\"https://github.com/CM-1-NEW/SNNW\" xlink:type=\"simple\">https://github.com/CM-1-NEW/SNNW</ce:inter-ref>.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"28 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261658","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}

{"title":"Spatiotemporal dynamics in a periodic SIS epidemic model with Fokker–Planck-type diffusion","authors":"Kai Wang ,&nbsp;Hao Wang ,&nbsp;Jianshe Yu ,&nbsp;Ran Zhang","doi":"10.1016/j.cnsns.2025.109363","DOIUrl":"10.1016/j.cnsns.2025.109363","url":null,"abstract":"<div><div>To investigate the effects of seasonality and individual movement on disease transmission, we formulate a periodic SIS epidemic model with external supply governed by Fokker–Planck-type diffusion law in a spatially heterogeneous environment. A key feature of the model is the incorporation of Fokker–Planck-type diffusion to describe individual movement. We analyze the asymptotic profiles and uniform boundedness of the basic reproduction ratio <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> with respect to the dispersal rate by addressing challenges arising from periodicity and the diffusion mechanism. Under certain conditions, explicit upper bounds for the solution are derived following the comparison principle and invariant region theory. The threshold dynamics indicate that the disease-free <span><math><mi>θ</mi></math></span>-periodic solution is globally asymptotically stable as <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span> and the system becomes uniformly persistent as <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Numerical analysis demonstrates that increasing the dispersal of susceptible individuals can reduce the scale of infection. Furthermore, periodicity is shown to enhance disease persistence and induce greater complexity into the disease dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109363"},"PeriodicalIF":3.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219432","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}

{"title":"Mixed zero-sum game based dynamic event-triggered optimal control of multi-input nonlinear system with safety constraints","authors":"Chunbin Qin ,&nbsp;Zhongwei Wang ,&nbsp;Suyang Hou ,&nbsp;Mingyu Pang ,&nbsp;Guanghui Wang ,&nbsp;Ying Wang ,&nbsp;Jishi Zhang ,&nbsp;Xin Wang","doi":"10.1016/j.cnsns.2025.109376","DOIUrl":"10.1016/j.cnsns.2025.109376","url":null,"abstract":"<div><div>This paper investigates the optimal safe control problem for mixed zero-sum game (MZS)-based multi-input nonlinear systems under dynamic event-triggered control with safety constraints. First, by employing a barrier-function-based system transformation methodology, the safety-constrained MZS game problem is converted into an equivalent system formulation, thereby ensuring persistent satisfaction of safety constraints throughout system operation. Secondly, a new dynamic event-triggered control is proposed for the multi-input MZS game system to reduce the system’s resource consumption. Furthermore, solving the Hamilton-Jacobi-Bellman (HJB) equation associated with the mixed zero-sum game (MZS) allows determination of the system’s optimal control strategy. Moreover, a critic neural network algorithm based on the experience replay is proposed to more efficiently approximate the optimal control strategy. Finally, the single-link robotic arm is employed to confirm the feasibility of the suggested method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109376"},"PeriodicalIF":3.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220142","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}

{"title":"Differential constraints for hyperbolic systems through k−Riemann invariants","authors":"Alessandra Jannelli ,&nbsp;Natale Manganaro ,&nbsp;Alessandra Rizzo","doi":"10.1016/j.cnsns.2025.109379","DOIUrl":"10.1016/j.cnsns.2025.109379","url":null,"abstract":"<div><div>In this paper we develop a reduction procedure for determining exact wave solutions of first order quasilinear hyperbolic one-dimensional nonhomogeneous systems. The approach is formulated within the theoretical framework of the method of differential constraints and it makes use of the <span><math><mrow><mi>k</mi><mo>−</mo></mrow></math></span>Riemann invariants. The solutions obtained permit to characterize rarefaction waves also for nonhomogeneous models so that Riemann problems can be solved. Applications to the Euler system describing an ideal fluid with a source term are given.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109379"},"PeriodicalIF":3.8,"publicationDate":"2025-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219435","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}

{"title":"New primal-dual algorithm for convex-concave saddle point problems","authors":"Shuning Liu, Zexian Liu","doi":"10.1016/j.cnsns.2025.109377","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109377","url":null,"abstract":"Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems of the primal and dual variables are crucial to the convergence theory and numerical performance of primal-dual algorithms. By taking advantage of the information from the current and previous iterative points, we employ two convex combinations on all previously generated iterative points to generate two new proximal terms for the subproblems of the primal and dual variables. It is remarkable that the weight assigned to the latest iterative point is always significant with a lower bound of 0.75 and can approach 1 regardless of whether the convex coefficient is near 0 or 1. Based on two novel proximal terms, we present a new primal-dual algorithm for convex-concave saddle point problems with bilinear coupling term and establish its global convergence and an <mml:math altimg=\"si12.svg\"><mml:mrow><mml:mi mathvariant=\"script\">O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\">/</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> ergodic convergence rate. When either the primal function or the dual function is strongly convex, we accelerate the above proposed algorithm and show that the corresponding algorithm can achieve an <mml:math altimg=\"si13.svg\"><mml:mrow><mml:mi mathvariant=\"script\">O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\">/</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math> convergence rate. Since the conditions for the stepsizes of the proposed algorithm are related directly to the spectral norm of the linear transform, which is difficult to obtain in some applications, we also introduce a linesearch strategy for the above proposed primal-dual algorithm and establish its global convergence and an <mml:math altimg=\"si12.svg\"><mml:mrow><mml:mi mathvariant=\"script\">O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo linebreak=\"goodbreak\">/</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> ergodic convergence rate. Some numerical experiments are conducted on matrix game and LASSO problems by comparing with other state-of-the-art algorithms, which demonstrate the effectiveness of the proposed three primal-dual algorithms.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"122 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261661","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}

{"title":"Weak collocation networks: A deep learning approach to reconstruct stochastic dynamics from aggregate data","authors":"Zhitong Chen, Zhijun Zeng, Pipi Hu, Yi Zhu","doi":"10.1016/j.cnsns.2025.109360","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109360","url":null,"abstract":"Stochastic differential equations (SDEs) play a key role in modeling the dynamics of systems significantly influenced by random perturbations. In this work, we propose a novel Weak Collocation Networks(WCN) method to determine the hidden dynamics-namely, the drift and diffusion functions of an SDE-from aggregate data. This method employs efficient neural networks, particularly the Kolmogorov-Arnold network (KAN), to parameterize the unknown functions. Instead of using the conventional metric that compares the data distribution with the predicted distribution, we introduce an efficient physics-informed loss derived from the weak form of the Fokker-Planck equation. By leveraging Monte Carlo spatial integration and a linear multi-step method for temporal differentiation, our approach facilitates a rapid and accurate estimation of the Fokker-Planck equation residual directly from observational data. Moreover, through an adaptive selection method for sampling the test function, we can enhance the robustness of our method. Numerical experiments demonstrate the efficiency and accuracy of our method.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"11 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261662","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}

{"title":"Low-velocity impact response of rotating 2D-FGM annular plates with variable thickness","authors":"Yu-Hao Fan,&nbsp;Gui-Lin She","doi":"10.1016/j.cnsns.2025.109373","DOIUrl":"10.1016/j.cnsns.2025.109373","url":null,"abstract":"<div><div>In engineering applications, annular plates with non-uniform thickness profiles are widely used in various scenarios owing to their characteristics of reducing weight, optimizing material distribution, and maintaining sufficient stiffness and strength. However, the mechanical response of such structures is inherently more complex than that of uniformly thick plates due to the variation in geometric shape. Meanwhile, this complexity is further compounded by the unclear mechanisms governing how bidirectional functionally graded materials (2D-FGMs) and local geometric imperfections affect low-velocity impact responses in rotating variable-thickness annular plates. The present study investigates these nonlinear impact characteristics through a novel analytical framework. By synergistically combining the first-order shear deformation theory (FSDT) with the improved nonlinear Hertz contact theory, the nonlinear governing equations of the plate are derived. The degradation model is validated to ensure the correctness of the proposed model. Finally, numerical analysis is conducted using the Runge-Kutta method to investigate the effects of different parameters, such as material gradient index, thickness coefficient, impact location, and local imperfections, on the nonlinear low-velocity impact response characteristics of the annular plates.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109373"},"PeriodicalIF":3.8,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220141","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}

{"title":"On equilateral central configurations in the 1+4-body problem","authors":"Martha Alvarez–Ramírez ,&nbsp;Esther Barrabés ,&nbsp;Josep M. Cors","doi":"10.1016/j.cnsns.2025.109365","DOIUrl":"10.1016/j.cnsns.2025.109365","url":null,"abstract":"<div><div>We investigate central configurations in the planar five-body problem with one dominant mass. The remaining four masses, referred to as coorbital satellites, are infinitesimal and positioned along a circle centered at the big mass. We focus on stacked relative equilibria in which the central body and two fixed satellites form an equilateral triangle, while the two remaining satellites occupy distinct positions on the unit circle. In the limiting case when the small masses tend to zero, the problem naturally divides into three scenarios depending on the location of these remaining bodies relative to the arc formed by the two fixed satellites. We show that the first case, in which both satellites lie inside the arc, cannot occur under the positivity constraint on the masses. The second case, where one satellite lies inside the arc and the other outside, admits solutions that we characterize in detail, while the third case, with both satellites outside the arc, leads to a richer family of admissible configurations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109365"},"PeriodicalIF":3.8,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219430","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}

{"title":"Acoustic black hole beam structure with dry friction energy dissipation: Conceptual modeling, solution method, and analysis of effect","authors":"Tichang Jia, Chen Chen, Jie Liu, Yulin Jiang, Zhipeng Lyu, Chaofeng Li","doi":"10.1016/j.cnsns.2025.109374","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109374","url":null,"abstract":"The acoustic black hole(ABH) beam can collect vibrational energy through its geometric structure. Therefore, it has great potential for application in energy collection and vibration suppression. Damping layers are usually introduced on ABH structures to attenuate vibration energy. However, the thickness of the damping layer may affect the energy harvesting and vibration attenuation effect. Therefore, this paper used friction damper components instead of damping layers to dissipate gathered energy and proposed a dry friction-damping ABH beam structure. Established a dynamic model of the ABH beam structure by using the assumed modal method. Using the LuGre model to characterize the force of friction elements. The dynamic response was solved by using the proposed finite difference time-frequency domain harmonic balance method. Then, the reduction effectiveness and superiority of the dry friction damping ABH beam structure were verified. The parameters affecting the vibration reduction effect were analyzed. The results indicate that the dry friction damping vibration reduction structure proposed in this paper can attenuate vibration amplitudes more effectively than the damping layer. A higher friction coefficient is more favorable for vibration attenuation within a certain range of preload. The vibration reduction method proposed in this article can achieve good vibration attenuation effects under various power laws, indicating that this method can also effectively attenuate vibration amplitude without optimizing the ABH shape.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"20 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145261698","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}