Communications in Nonlinear Science and Numerical Simulation最新文献_第7页

Unconditional error analysis of an element-free Galerkin method for the nonlinear Schrödinger equation 非线性Schrödinger方程无单元伽辽金法的无条件误差分析

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-08 DOI: 10.1016/j.cnsns.2025.109103

Xiaolin Li , Haiyun Dong

引用次数: 0

Model-free forecasting of rogue waves using Reservoir Computing 利用水库计算的无模式异常波预报

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-08 DOI: 10.1016/j.cnsns.2025.109087

Abrari Noor Hasmi, Hadi Susanto

{"title":"Model-free forecasting of rogue waves using Reservoir Computing","authors":"Abrari Noor Hasmi, Hadi Susanto","doi":"10.1016/j.cnsns.2025.109087","DOIUrl":"10.1016/j.cnsns.2025.109087","url":null,"abstract":"<div><div>Recent research has demonstrated Reservoir Computing’s capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir Computing in capturing rogue wave dynamics from the nonlinear Schrödinger equation, a challenging Hamiltonian system with modulation instability. The model-free approach learns from breather simulations with five unstable modes. A properly tuned parallel Echo State Network can predict dynamics from two distinct testing datasets. The first set is a continuation of the training data, whereas the second set involves a higher-order breather. An investigation of the one-step prediction capability shows remarkable agreement between the testing data and the models. Furthermore, we show that the trained reservoir can predict the propagation of rogue waves over a relatively long prediction horizon, despite facing unseen dynamics. Finally, we introduce a method to significantly improve the Reservoir Computing prediction in autonomous mode, enhancing its long-term forecasting ability. These results advance the application of Reservoir Computing to spatio-temporal Hamiltonian systems and highlight the critical importance of phase space coverage in the design of training data.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109087"},"PeriodicalIF":3.4,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621961","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}

引用次数: 0

Nonlinear dynamics characteristics of giant magnetostrictive thin-film micro-actuators with cracks 含裂纹的超磁致伸缩薄膜微致动器的非线性动力学特性

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-06 DOI: 10.1016/j.cnsns.2025.109127

Xiaohuan Li , Yongyao Chen , Wei Gao , Lianjia Zhao

{"title":"Nonlinear dynamics characteristics of giant magnetostrictive thin-film micro-actuators with cracks","authors":"Xiaohuan Li , Yongyao Chen , Wei Gao , Lianjia Zhao","doi":"10.1016/j.cnsns.2025.109127","DOIUrl":"10.1016/j.cnsns.2025.109127","url":null,"abstract":"<div><div>Precision micro-actuators are the core components of micro mechanical systems, and the presence of cracks affects the dynamic behavior and performance of micro-actuators. In this paper, a time-varying stiffness model is proposed to describe the effect of cracks on the dynamic characteristics of giant magnetostrictive thin-film micro-actuators, and the dynamic model of Galfenol/Si film micro-actuator is established with Hamilton's principle. The nonlinear vibration characteristics of the crack brake under simple harmonic excitation and stochastic excitation are investigated separately to obtain the stability conditions of the system. The effects of system parameters on the dynamic characteristics are analyzed. The results show that under simple harmonic excitation, the presence of cracks weakens the stability of the system, while under random excitation, cracks enhance the stability of the system. The increase the damping especially the higher order nonlinear damping term can improve the stability of the shaker. The results provide a basis for the engineering application of Galfenol/Si film micro actuator.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109127"},"PeriodicalIF":3.4,"publicationDate":"2025-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621936","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}

引用次数: 0

Entropy solutions for elliptic problems in generalized ψ-Hilfer fractional derivative frameworks involving a γ(x)-Laplacian-type operator 涉及γ(x)- laplace型算子的广义ψ-Hilfer分数阶导数框架中椭圆问题的熵解

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-05 DOI: 10.1016/j.cnsns.2025.109095

Abdelaziz Sabiry, Ghizlane Zineddaine, Abderrazak Kassidi

{"title":"Entropy solutions for elliptic problems in generalized ψ-Hilfer fractional derivative frameworks involving a γ(x)-Laplacian-type operator","authors":"Abdelaziz Sabiry, Ghizlane Zineddaine, Abderrazak Kassidi","doi":"10.1016/j.cnsns.2025.109095","DOIUrl":"10.1016/j.cnsns.2025.109095","url":null,"abstract":"<div><div>This article investigates a class of <span><math><mi>Ψ</mi></math></span>-Hilfer generalized fractional nonlinear elliptic equations incorporating a <span><math><mrow><mi>γ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>-Laplacian operator, inspired by capillarity phenomena. The study extends the theoretical understanding of <span><math><mrow><mi>γ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>-Laplacian operators and highlights their significance in modeling capillary-induced processes. A key contribution lies in the analysis of a <span><math><mrow><mi>γ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>-Laplacian-like operator, which introduces more intricate nonlinearities compared to the classical Laplacian and <span><math><mi>γ</mi></math></span>-Laplacian. Furthermore, the approach is based on <span><math><mi>Ψ</mi></math></span>-Hilfer fractional derivatives, providing a more generalized framework for fractional calculus and enabling a better understanding of the nonlocal effects associated with the problem under consideration.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109095"},"PeriodicalIF":3.4,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144587797","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}

引用次数: 0

Energy- and mass-preserving ESAV/Lagrange multiplier Hermite spectral scheme for coupled nonlinear Klein–Gordon equations in unbounded domains 无界域中耦合非线性Klein-Gordon方程的保持能量和质量的ESAV/Lagrange乘子Hermite谱格式

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-05 DOI: 10.1016/j.cnsns.2025.109067

Xiaohao Zhang, Liquan Mei, Shimin Guo

{"title":"Energy- and mass-preserving ESAV/Lagrange multiplier Hermite spectral scheme for coupled nonlinear Klein–Gordon equations in unbounded domains","authors":"Xiaohao Zhang, Liquan Mei, Shimin Guo","doi":"10.1016/j.cnsns.2025.109067","DOIUrl":"10.1016/j.cnsns.2025.109067","url":null,"abstract":"<div><div>We construct an efficient and accurate numerical scheme which preserves exactly the mass and the original energy for solving the coupled nonlinear Klein–Gordon equations in unbounded domain <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. To overcome the drawback of the ESAV method not being able to preserve the mass, we ingeniously combine the ESAV method with the Lagrange multiplier approach to rewrite the original equations into a new equivalent reformulation. Then, we employ the Crank–Nicolson method coupled with the Adams–Bashforth method for temporal discretization and utilize Hermite–Galerkin spectral scheme for spatial discretization. To implement the fully discrete scheme, we only need to solve two linear systems with constant coefficients and a quadratic algebraic equation at each time step. We propose an adaptive time-stepping strategy based on the variation of scalar field functions to significantly improve the efficiency without sacrificing accuracy. We present ample numerical tests to validate the characteristics of the proposed scheme in 1D/2D, and apply the scheme to simulate the nonlinear dynamics of solitons in 3D.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109067"},"PeriodicalIF":3.4,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572271","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}

引用次数: 0

Bifurcation of sub-harmonic solutions of some 4-dimensional piecewise smooth near-Hamiltonian systems 一类四维分段光滑近哈密顿系统次调和解的分岔

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-05 DOI: 10.1016/j.cnsns.2025.109112

Tingting Quan , Min Sun , Ziyu Guo , Hua Zhang

{"title":"Bifurcation of sub-harmonic solutions of some 4-dimensional piecewise smooth near-Hamiltonian systems","authors":"Tingting Quan , Min Sun , Ziyu Guo , Hua Zhang","doi":"10.1016/j.cnsns.2025.109112","DOIUrl":"10.1016/j.cnsns.2025.109112","url":null,"abstract":"<div><div>The analysis of periodic solutions in high-dimensional dynamical piecewise smooth systems under non-autonomous perturbations is critical for understanding complex phenomena in engineering and physics. This paper investigates the bifurcation of subharmonic solutions of 4-dimensional piecewise smooth near-Hamiltonian systems with non-autonomous perturbations and a two-region partition separated by a hyperplane. By establishing a dynamic curvilinear coordinate system, we develop an analytical approach for computing the Poincaré map, from which the extended Melnikov function suitable for such systems is derived. Through analysis of the extended Melnikov function, we derive necessary conditions and sufficient conditions for the bifurcation of subharmonic solutions, encompassing both degenerate and non-degenerate resonance cases. The present result generalizes some of the known results on the Melnikov theory with respect to both dimension and system formulation. To demonstrate the practical application of our theoretical work, we implement the extended Melnikov method to analyze the bifurcation and number of subharmonic solutions of a two-degree-of-freedom nonlinear energy sink system. Our results reveal that the system can support up to 3 distinct subharmonic solutions, and we provide explicit parameter control conditions governing this behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109112"},"PeriodicalIF":3.4,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621840","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}

引用次数: 0

Spatiotemporal transmission dynamics and optimal regional control of a spatial heterogeneity reaction–diffusion schistosomiasis model 空间异质性反应-扩散血吸虫病模型的时空传播动态及最优区域控制

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-04 DOI: 10.1016/j.cnsns.2025.109097

Tong Chen , Longhao Chen , Peng Wu

{"title":"Spatiotemporal transmission dynamics and optimal regional control of a spatial heterogeneity reaction–diffusion schistosomiasis model","authors":"Tong Chen , Longhao Chen , Peng Wu","doi":"10.1016/j.cnsns.2025.109097","DOIUrl":"10.1016/j.cnsns.2025.109097","url":null,"abstract":"<div><div>In this paper, to explore the effects of heterogeneous diffusion and optimal regional control on schistosomiasis transmission, we establish a reaction–diffusion schistosomiasis model incorporating spatial heterogeneity and general incidence rates. We first demonstrate the well-posedness of the model using classical theory of parabolic systems. Then, we derive the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and investigate its threshold-type implications for the global dynamics of disease spread. Furthermore, under certain conditions, we analyze the asymptotic behavior of <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, with particular attention to its monotonicity with respect to the case of degenerate heterogeneous diffusion coefficients. Considering the regional characteristics of schistosomiasis epidemics, we formulate an optimal regional control problem aimed at minimizing the total number of susceptible and infected individuals, as well as the associated treatment costs. Finally, we conduct two-dimensional numerical simulations. On one hand, we confirm the global dynamics of disease persistence when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. On the other hand, by implementing optimal regional control strategies under two distinct initial outbreak scenarios, we demonstrate effective containment of disease spread. In particular, when the infection originates near the center of the spatial domain, targeted interventions around the source significantly reduce transmission. Our work suggests that optimal regional control can effectively suppress schistosomiasis transmission at minimal cost, offering valuable insights for public health authorities in designing efficient control strategies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109097"},"PeriodicalIF":3.4,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572270","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}

引用次数: 0

An improved adaptive sliding mode controller for generating periodic motions in mechanical systems – A model-free approach 一种用于产生机械系统周期运动的改进自适应滑模控制器——一种无模型方法

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-04 DOI: 10.1016/j.cnsns.2025.109128

Swapnil Mahadev Dhobale, Shyamal Chatterjee

{"title":"An improved adaptive sliding mode controller for generating periodic motions in mechanical systems – A model-free approach","authors":"Swapnil Mahadev Dhobale, Shyamal Chatterjee","doi":"10.1016/j.cnsns.2025.109128","DOIUrl":"10.1016/j.cnsns.2025.109128","url":null,"abstract":"<div><div>This article presents a novel methodology for generating periodic motions in mechanical systems through a two-step approach. First, a reference trajectory is autonomously generated using a harmonic limit cycle oscillator, which produces pure harmonic signals with specified frequency and unit amplitude. To represent arbitrary smooth periodic signals, a new Fourier-Chebyshev Transform (FCT) is introduced. This transform expresses the desired trajectory as a polynomial in the state variables of the oscillator, with coefficients obtained by applying the FCT to the Fourier components of the target signal. The proposed approach is envisioned as a potential central pattern generator (CPG). In the second step, a synchronization controller is designed to ensure stable and efficient tracking of the reference oscillation by the mechanical system. A model-free, modified sliding mode control (MSMC) strategy is proposed, which demonstrates superior performance compared to ideal sliding mode control (ISMC) and optimized super-twisting SMC, particularly in terms of convergence speed, tracking accuracy, and control effort. Additionally, a gain adaptation mechanism is employed to enhance robustness against system uncertainties and external disturbances. The effectiveness of the proposed methodology is validated through multiple simulations and experimental results involving a pendulum system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109128"},"PeriodicalIF":3.4,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621841","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}

引用次数: 0

Dynamics on vortex-induced vibration suppression of a flexible cable by tuned mass damper 调谐质量阻尼器抑制柔性索涡激振动的动力学研究

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-03 DOI: 10.1016/j.cnsns.2025.109129

Dengyu Qian , Yunyue Cong , Houjun Kang , Xiaoyang Su

{"title":"Dynamics on vortex-induced vibration suppression of a flexible cable by tuned mass damper","authors":"Dengyu Qian , Yunyue Cong , Houjun Kang , Xiaoyang Su","doi":"10.1016/j.cnsns.2025.109129","DOIUrl":"10.1016/j.cnsns.2025.109129","url":null,"abstract":"<div><div>Tuned mass dampers (TMDs) are commonly installed to suppress vortex-induced vibrations in flexible cables, but their effectiveness is often limited by an insufficient understanding of the fluid-structure coupling mechanisms. To this end, a refined wake-cable-TMD coupled dynamic model that employs a van der Pol wake oscillator to simulate the fluid force caused by vortex shedding is proposed in this paper, with explicit analysis of energy transfer and 1:1 internal resonance dynamics under primary resonance conditions. Motion equations of the coupled system are derived using the extended Hamilton principle, and the corresponding reduced-order model is developed through Galerkin discretization. The key step lies in the analytical solution of the nonlinear system via the method of multiple scales (MMS), which reveals steady-state slow dynamics through modulation equations governing the interactions between the wake, cable, and TMD, an aspect rarely addressed in prior studies. Additionally, critical aerodynamic parameters of the cable are obtained through two-dimensional Computational Fluid Dynamics (CFD) simulation, ensuring empirical validity. The results demonstrate that the TMD not only absorbs the vibration energy transferred to the cable from the wake but also alters the cable’s dynamic properties, causing a shift in the frequency ‘lock-in’ region and exhibiting dual-resonance peaks in frequency response curves due to frequency-splitting phenomena. Parametric analyses further show how TMD stiffness, damping, and placement influence system stability and vibration suppression effect.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109129"},"PeriodicalIF":3.4,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580757","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}

引用次数: 0

Nonlinear resonance and attractors coexistence in high-speed train helical gear systems under multi-source excitation 多源激励下高速列车斜齿轮系统的非线性共振和吸引子共存

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-07-03 DOI: 10.1016/j.cnsns.2025.109124

Yeping Yuan , Wen Zhang , Junguo Wang

{"title":"Nonlinear resonance and attractors coexistence in high-speed train helical gear systems under multi-source excitation","authors":"Yeping Yuan , Wen Zhang , Junguo Wang","doi":"10.1016/j.cnsns.2025.109124","DOIUrl":"10.1016/j.cnsns.2025.109124","url":null,"abstract":"<div><div>Helical gear transmission systems are critical components for power transmission in high-speed trains, significantly influencing operational stability and ride comfort. Torsional vibrations in gear systems primarily arise from internal meshing excitations and unstable load fluctuations at both ends. Addressing torsional resonance and global stability under internal and external excitations remains an urgent challenge. This paper aims to investigate the nonlinear resonance responses and global dynamic characteristics of torsional vibration in helical gear systems under multi-source excitation. A single-degree-of-freedom torsional vibration model is established for high-speed train gear systems, incorporating nonlinear factors such as backlash, time-varying meshing stiffness (TVMS), static transmission error, and external load fluctuations. The method of multiple scales is employed to derive approximate solutions and amplitude-frequency responses. Nonlinear resonance behaviors, including primary resonance, super-harmonic resonance, sub-harmonic resonance, and combination resonance, are analyzed. Global analysis via the cell mapping method reveals the effects of rotational speed, helix angle, and external load fluctuation amplitude on attractor coexistence and basin of attraction evolution. Furthermore, rich coexisting dynamics are revealed through the bifurcation diagrams of the two-parameter domain. These analytical results provide a theoretical foundation for parametric design and subsequent multi-stable control strategy development in high-speed train gear systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109124"},"PeriodicalIF":3.4,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596771","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}

引用次数: 0