Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"∂̄-dressing method for the coupled third-order flow equation of the Kaup–Newell system","authors":"Jin-Jin Mao","doi":"10.1016/j.cnsns.2025.108841","DOIUrl":"10.1016/j.cnsns.2025.108841","url":null,"abstract":"<div><div>In this article, we investigate the nonlinear spectral properties of the coupled third-order flow of the Kaup–Newell (TOFKN) system by formulating a local matrix <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-equation with non-normalized boundary conditions and two linear constraint equations. Furthermore, we derive a coupled Kaup–Newell hierarchy with sources using recursive operator. By employing a specially designed spectral transformation matrix and the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method, we construct the <span><math><mi>N</mi></math></span>-soliton solutions of the coupled TOFKN system, providing explicit expressions for the one- and two-soliton solutions. These findings demonstrate the effectiveness of the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method in capturing the complex nonlinear dynamics of the TOFKN system, offering new insights into its soliton interactions and stability properties.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108841"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943244","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":"Refining extinction criteria in a complex multi-stage epidemic system with non-Gaussian Lévy noise","authors":"Yassine Sabbar","doi":"10.1016/j.cnsns.2025.108911","DOIUrl":"10.1016/j.cnsns.2025.108911","url":null,"abstract":"<div><div>This paper proposes a new approach for analyzing extinction conditions in multi-stage epidemic models, incorporating stochastic noises to account for sudden environmental or population-level changes that influence infection transmission. By utilizing an <span><math><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional perturbed system that captures both gradual amelioration and proportional jumps, the research establishes sharp extinction criteria, refining the assumptions typically found in existing literature. Moving away from classical methods that rely on ergodicity, this framework employs moment analysis of the average solution time for an auxiliary equation, effectively addressing the challenges arising from the lack of an explicit expression of the invariant measure. The theoretical results are compared with those from previous studies, and numerical simulations, particularly focused on AIDS/HIV, serve to confirm and reinforce the findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108911"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941879","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":"Error analysis of a fractional-step method for reactive fluid flows with Arrhenius activation energy","authors":"Mofdi El-Amrani ,&nbsp;Anouar Obbadi ,&nbsp;Mohammed Seaid ,&nbsp;Driss Yakoubi","doi":"10.1016/j.cnsns.2025.108867","DOIUrl":"10.1016/j.cnsns.2025.108867","url":null,"abstract":"<div><div>Propagation problems of reaction fronts in viscous fluids are crucial in many industrial and chemical engineering processes. The interactions between the reaction properties and the fluid dynamics yield a complex and nonlinear model of Navier–Stokes equations for the flow with a strong coupling with two reaction–advection–diffusion equations for the temperature and the degree of conversion. To alleviate difficulties related to the numerical approximation of such systems, we propose a fractional-step method to split the problem into several substeps, and based on a viscosity-splitting approach that separates the convective terms from the diffusion terms during the time integration. A first-order scheme is employed for the time integration of each substep of the proposed fractional-step method. The proposed method also preserves the full original boundary conditions for the velocity which eliminates any potential inconsistencies on the pressure, and it allows for nonhomogeneous Dirichlet and Neumann boundary conditions for the temperature and degree of conversion that are physically more appealing. In the present work, we perform an error analysis and provide error estimates for all involved solutions in their relevant norms. A rigorous stability analysis is also carried out in this study and the proposed method is demonstrated to be consistent and stable with no restrictions on the time step. Numerical results obtained for a problem with known analytical solutions are presented to verify the theoretical analysis and to assess the performance of the proposed method. The method is also implemented for solving a two-dimensional flame-like propagation problem in viscous fluids. The obtained computational results for both examples support the theoretical expectations for a stable and accurate numerical solver for reactive fluids with Arrhenius activation energy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108867"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936252","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":"An innovative low-order H1-Galerkin mixed finite element framework for superconvergence analysis in nonlinear Klein–Gordon equations","authors":"Yanmi Wu,&nbsp;Xin Ge","doi":"10.1016/j.cnsns.2025.108912","DOIUrl":"10.1016/j.cnsns.2025.108912","url":null,"abstract":"<div><div>A <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Galerkin mixed finite element method (MFEM) is explored for solving the nonlinear Klein–Gordon equation, utilizing the lower-order bilinear element paired with the zero-order Raviart–Thomas element <span><math><mrow><mo>(</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>11</mn></mrow></msub><mo>+</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>10</mn></mrow></msub><mspace></mspace><mo>×</mo><mspace></mspace><msub><mrow><mi>Q</mi></mrow><mrow><mn>01</mn></mrow></msub><mo>)</mo></mrow></math></span>. The existence and uniqueness of the solutions for the discretized system are rigorously established. By exploiting the integral identity associated with the bilinear element, a superconvergence estimate linking the interpolation and the Riesz projection is derived. In the semi-discrete framework, the supercloseness of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> is achieved for the primary variable <span><math><mi>u</mi></math></span> in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm and for the auxiliary variable <span><math><mrow><mover><mrow><mi>p</mi></mrow><mo>→</mo></mover><mo>=</mo><mo>∇</mo><mi>u</mi></mrow></math></span> in the <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mtext>div</mtext><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> norm, respectively. Additionally, global superconvergence results are obtained through an interpolation-based postprocessing method. Moving to the fully discrete formulation, a second-order scheme is introduced, which exhibits the supercloseness of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>h</mi></math></span> represents the subdivision parameter and <span><math><mi>τ</mi></math></span> the time increment. Finally, the numerical experiments are conducted to confirm the validity of the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108912"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936250","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":"Using Lagrangian descriptors to reveal the phase space structure of dynamical systems described by fractional differential equations: Application to the Duffing oscillator","authors":"Dylan Theron ,&nbsp;Hadi Susanto ,&nbsp;Makrina Agaoglou ,&nbsp;Charalampos Skokos","doi":"10.1016/j.cnsns.2025.108848","DOIUrl":"10.1016/j.cnsns.2025.108848","url":null,"abstract":"<div><div>We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian descriptors method to study the phase space structure of the unforced and undamped Duffing oscillator when fractional-order differential equations govern its time evolution. Our study considers the Riemann–Liouville and the Caputo fractional derivatives. We use the Grünwald–Letnikov derivative, which is an operator represented by an infinite series, truncated suitably to a finite sum as a finite difference approximation of the Riemann–Liouville operator, along with a correction term that approximates the Caputo fractional derivative. While there is no issue with forward-time integrations needed for the evaluation of Lagrangian descriptors, we discuss in detail ways to perform the non-trivial task of backward-time integrations and implement two methods for this purpose: a ‘nonlocal implicit inverse’ technique and a ‘time-reverse inverse’ approach. We analyze the differences in the Lagrangian descriptors results due to the two backward-time integration approaches, discuss the physical significance of these differences, and eventually argue that the ‘nonlocal implicit inverse’ implementation of the Grünwald–Letnikov fractional derivative manages to reveal the phase space structure of fractional-order dynamical systems correctly.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108848"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067177","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":"Disturbance observer-based H∞ quantized fuzzy control of nonlinear delayed parabolic PDE systems","authors":"Xiaoyu Sun ,&nbsp;Chuan Zhang ,&nbsp;Huaining Wu ,&nbsp;Xianfu Zhang","doi":"10.1016/j.cnsns.2025.108909","DOIUrl":"10.1016/j.cnsns.2025.108909","url":null,"abstract":"<div><div>This research presents a novel quantized fuzzy control technique based on Luenberger-like disturbance observer for a class of nonlinear delayed parabolic partial differential equation (PDE) systems, which are influenced by two distinct types of disturbances. To begin with, the PDE system is decomposed using the Galerkin approach, resulting in a finite-dimensional slow ordinary differential equation (ODE) subsystem and an infinite-dimensional fast ODE subsystem. Then, the slow system which effectively characterizes the active mechanical behavior of the initial model is fuzzified by the Takagi–Sugeno fuzzy technique to obtain a relatively accurate model. Subsequently, based on disturbance observer, three types of quantized fuzzy controllers are devised to ensure that the system become semi-globally uniformly ultimately bounded. Furthermore, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance control problem with different quantizers is investigated in this study. Lastly, the numerical simulation demonstrates the effectiveness of the three quantizers.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108909"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929618","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":"Resilient discontinuous event-triggering control for exponential stabilization of memristive neural networks under denial-of-service attacks","authors":"Yanyan Ni,&nbsp;Zhen Wang","doi":"10.1016/j.cnsns.2025.108903","DOIUrl":"10.1016/j.cnsns.2025.108903","url":null,"abstract":"<div><div>This paper studies the exponential stabilization issue of memristive neural networks (MNNs) in the presence of denial-of-service (DoS) attacks by using an event-triggering scheme. Unlike the existing event-triggering strategies, not only does the devised resilient discontinuous event-triggering (RDET) scheme avoid the Zeno phenomenon and reduce network communication resource utilization, but can it effectively deal with the non-periodic DoS attacks. In the joint framework of RDET control and DoS attacks, a closed-loop MNNs system is established. Then, to address the attacks in different scenarios, two different-interval-dependent functionals are established. The continuity of functionals improves the anti-attack rate compared with the previous work. Moreover, by using a combination of the convex combination and the estimation techniques, the exponential stabilization results are deduced and a secure controller associated with event-triggering parameters are co-designed. Finally, simulations are carried out to demonstrate the effectiveness of the derived stabilization results and the practical advantages of the proposed RDET scheme subject to DoS attacks.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108903"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929617","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":"The dynamic corridor of regolith transportation near a spinning-up asteroid","authors":"Yutian Wu ,&nbsp;Zhijun Song ,&nbsp;Xiaojing Zhang ,&nbsp;Yang Yu ,&nbsp;Jing Lv","doi":"10.1016/j.cnsns.2025.108905","DOIUrl":"10.1016/j.cnsns.2025.108905","url":null,"abstract":"<div><div>The transport of regolith material has been confirmed by in situ exploration missions to asteroids like Itokawa, Ryugu and Bennu, providing evidences for the topographic evolution of these minor planets. This paper studies the migration of disturbed regolith materials across the asteroid surface from the viewpoint of nonlinear dynamics. We propose a simplified two-dimensional model that captures the dynamics of the regolith migration in a strongly perturbed environment, considering the non-spherical gravitational field induced by a massive body of irregular shape. We choose the shape of the equatorial cross-section of asteroid (101955) Bennu as a representative case. The transport paths of surface particles in terms of the spin-up process are identified. By checking the accessible/forbidden regions in the vicinity of the asteroid, we find that at low spin rates, regolith particles are confined to the vicinity of their initial positions and the motion area is sketched by the boundary of the zero-velocity curve. As the spin rate increases, we observe the formation of a notch that connects the two divided parts of the accessible regions, which creates a C-shaped corridor. Through this corridor, particles can enter cycling orbits around the asteroid, forming a continuous flow of mass movement. The long-term transport tendency of the surface material is found to be governed by this corridor. A higher spin rate enhances the occurrence of large-scale transport of particles across the asteroid surface. Using the methodology developed in this paper, we provide a perspective on the long-term transport dynamics of regolith materials, and it helps us to achieve a macro-analysis of the mass redistribution during the slow spin-up process of an asteroid.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108905"},"PeriodicalIF":3.4,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941881","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":"A maximum bound principle-preserving, second-order BDF scheme with variable steps for the generalized Allen–Cahn equation","authors":"Xiaohan Zhu ,&nbsp;Yuezheng Gong ,&nbsp;Yushun Wang","doi":"10.1016/j.cnsns.2025.108897","DOIUrl":"10.1016/j.cnsns.2025.108897","url":null,"abstract":"<div><div>The maximum bound principle (MBP) is a crucial characteristic for a board class of semilinear parabolic equations, making it essential to preserve this feature in numerical simulations, particularly for problems involving degenerate mobility and logarithmic potential function. In this paper, we focus on the nonuniform second-order backward differentiation formula (BDF2) for the Allen–Cahn (AC) model with general potential and variable mobility. With moderate restrictions on the time step and a condition on the time-step ratio, the nonuniform BDF2 scheme has been shown to satisfy the discrete MBP. The newly improved kernels recombination technique and MBP-preserving iteration technique significantly contribute to this analysis. This work represents the first result of a nonuniform BDF2 scheme that preserves the MBP for AC-type equations with a logarithmic potential function. With the discrete MBP, the maximum norm convergence analysis is obtained without requiring any Lipschitz conditions on the nonlinear bulk force. Additionally, various numerical experiments are conducted for the generalized AC model, incorporating an adaptive time-stepping algorithm.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108897"},"PeriodicalIF":3.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918290","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":"A virtual element constructed based on a class of quasi-orthogonal polynomials and its application to fourth-order elliptic problems","authors":"Jianjun Wan,&nbsp;Jiaxin Wei,&nbsp;Yuanjiang Xu,&nbsp;Shilei Xu,&nbsp;Chunyan Niu","doi":"10.1016/j.cnsns.2025.108884","DOIUrl":"10.1016/j.cnsns.2025.108884","url":null,"abstract":"<div><div>In order to improve an existing classical virtual element for the fourth-order elliptic problem, we propose a special class of quasi-orthogonal polynomials and then construct a new type of numerical integration formula based on the polynomials. The special feature of the formula is that it uses the function values and the derivative values of the integrand at the endpoint of the interval, which is of some practicality in virtual element construction and other occasions. Then, we replace the edge integral degrees of freedom (DoFs) in the existing virtual element with the function values at the integral points of the above formula, and propose a modified virtual element for solving the fourth-order elliptic problem. We analyze the convergence and computability of the modified virtual element, and the results show that the element has the characteristics of simpler programming implementation and lower computational complexity while maintaining the original convergence order. Finally, numerical results are given to verify the convergence of the element in solving the fourth-order elliptic problem.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108884"},"PeriodicalIF":3.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143911780","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}