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Communications in Nonlinear Science and Numerical Simulation最新文献

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Existence of traveling pulses for a diffusive prey–predator model with strong Allee effect and weak distributed delay 具有强Allee效应和弱分布延迟的扩散捕食-捕食模型的行脉冲存在性
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-16 DOI: 10.1016/j.cnsns.2025.108596
Yuhang Wu , Mingkang Ni
{"title":"Existence of traveling pulses for a diffusive prey–predator model with strong Allee effect and weak distributed delay","authors":"Yuhang Wu ,&nbsp;Mingkang Ni","doi":"10.1016/j.cnsns.2025.108596","DOIUrl":"10.1016/j.cnsns.2025.108596","url":null,"abstract":"<div><div>In this article, we investigate the existence of traveling pulses in a diffusive prey–predator model with a strong Allee effect and weak distributed delay. Assuming that the growth and death rates of the predator are much smaller than those of the prey and that the average delay is small, we transform the model into a singularly perturbed problem with a three-time scale structure. Using generalized rotated vector field theory, geometric singular perturbation theory, and the phase plane method, we demonstrate the existence of a homoclinic orbit depending on the intermediate-slow system. In particular, we obtain the positions of the transverse heteroclinic orbit in the intermediate layer problem and provide explicit expressions for the associated heteroclinic orbit and wave speed. Additionally, we construct possible singular homoclinic orbits of the model and show the persistence of these orbits for two different small perturbation parameters.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108596"},"PeriodicalIF":3.4,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021248","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
Command-filter based predefined-time neural adaptive decentralized control for interconnected systems with dynamic uncertainties 基于命令滤波的动态不确定性互联系统自适应分散控制
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-15 DOI: 10.1016/j.cnsns.2025.108611
Zhucheng Liu , Feisheng Yang , Heng Li
{"title":"Command-filter based predefined-time neural adaptive decentralized control for interconnected systems with dynamic uncertainties","authors":"Zhucheng Liu ,&nbsp;Feisheng Yang ,&nbsp;Heng Li","doi":"10.1016/j.cnsns.2025.108611","DOIUrl":"10.1016/j.cnsns.2025.108611","url":null,"abstract":"<div><div>This article studies the predefined-time controller construction problem for non-strict feedback nonlinear large-scale interconnected systems including unmodeled dynamics and dynamic disturbances. The uncertain nonlinearities and interconnections in the studied systems are universally approximated by neural networks. The observable dynamic signals created by the constructed auxiliary systems are utilized to alleviate the impacts of unmodeled state dynamics. Then, a neural adaptive predefined-time decentralized controller is developed via command filtered backstepping technology. The convergence time bound by the proposed control strategy is more flexible than conventional fixed-time control method. Moreover, through adding the compensation signal terms to the entire Lyapunov energy function, all variables in the controlled system are proved to be predefined-time bounded. The simulation shows the validity and superiority of the presented controller.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108611"},"PeriodicalIF":3.4,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021208","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
The primary resonance of a Duffing oscillator with a restoring force of fractional-order derivatives by the extended Galerkin method 用扩展伽辽金方法研究了具有分数阶导数恢复力的Duffing振子的主共振
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-15 DOI: 10.1016/j.cnsns.2025.108619
Chencheng Lian , Baochen Meng , Huimin Jing , Hui Chen , Fang Xie , Ji Wang
{"title":"The primary resonance of a Duffing oscillator with a restoring force of fractional-order derivatives by the extended Galerkin method","authors":"Chencheng Lian ,&nbsp;Baochen Meng ,&nbsp;Huimin Jing ,&nbsp;Hui Chen ,&nbsp;Fang Xie ,&nbsp;Ji Wang","doi":"10.1016/j.cnsns.2025.108619","DOIUrl":"10.1016/j.cnsns.2025.108619","url":null,"abstract":"<div><div>The nonlinear vibrations have wide appearances in many scientific and engineering problems to be solved by various techniques to satisfy requirements for solutions. With many different equations of nonlinear features, approximate methods have been suggested and tested to enable simple, accurate, and efficient solution procedures in dealing with increasingly complex problems. The introduction of fractional-order derivative as a restoring force in nonlinear vibration equations brought in advantages in dealing with some dissipation and excitation factors, but the complexity has also increased significantly, and the solution techniques are in strained testing for applicability and efficiency. To meet the challenges for newer solution techniques with a simpler procedure, the extended Galerkin method for nonlinear vibration analysis is applied to such problems with fractional-order derivatives through the expansion of integration interval to large number of periods, and approximate solutions of amplitudes are obtained and validated. This study demonstrates that the extended Galerkin method is an effective procedure for the nonlinear vibration equations with fractional-order derivative terms, expanding the application of the newer method and providing solutions with a simpler procedure.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108619"},"PeriodicalIF":3.4,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021207","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
Effects of pulse amplitude modulation on relaxation oscillations in the Duffing system 脉冲调幅对Duffing系统弛豫振荡的影响
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-14 DOI: 10.1016/j.cnsns.2025.108606
Jin Song , Mengke Wei , Wenjie Zuo , Xiujing Han , Qinsheng Bi
{"title":"Effects of pulse amplitude modulation on relaxation oscillations in the Duffing system","authors":"Jin Song ,&nbsp;Mengke Wei ,&nbsp;Wenjie Zuo ,&nbsp;Xiujing Han ,&nbsp;Qinsheng Bi","doi":"10.1016/j.cnsns.2025.108606","DOIUrl":"10.1016/j.cnsns.2025.108606","url":null,"abstract":"<div><div>This paper reports on the fast-slow dynamics induced by pulse amplitude modulation (PAM). Typically, PAM transmits information signals by altering the amplitude of the pulse signal, with the core concept being that the amplitude of the pulse sequence varies according to the input data. It was observed that introducing additional pulse excitation in the Duffing system results in a relaxation oscillation mode characterized by catastrophic jumps. Using the fast-slow analysis method, the generation mechanism of these relaxation oscillations was elucidated, wherein PAM results from the superposition of periodic cosine and periodic pulse signals. Subsequently, the cases of periodic cosine excitation, pulse excitation, and PAM excitation for a single slow variable were separately discussed. The study demonstrates that PAM plays a critical role in the fast-slow dynamics of the Duffing system. Specifically, changes in amplitude under pulse modulation lead to varying degrees of relaxation oscillation modes. For instance, low PAM induces a mode where conventional oscillations connected by catastrophic jumps alternate with a resting state. Moreover, when the amplitude crosses a certain critical value, it leads to a mode where relaxation oscillations connected by catastrophic jumps alternate with a resting state. Furthermore, when the modulation amplitude exceeds another critical value, it causes a transition in the resting state position, which is associated with the attraction domains at different amplitudes. Based on these findings, compound relaxation oscillation modes were revealed. Finally, comparisons of circuit simulation experiments validated the results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108606"},"PeriodicalIF":3.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021210","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
Some practical regards on the application of the physics-informed sparse identification for strongly NESs 基于物理信息的强NESs稀疏识别的一些实际应用
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-14 DOI: 10.1016/j.cnsns.2025.108610
Qinghua Liu , Zehao Hou , Ying Zhang , Xiaojun Xu , Dong Jiang
{"title":"Some practical regards on the application of the physics-informed sparse identification for strongly NESs","authors":"Qinghua Liu ,&nbsp;Zehao Hou ,&nbsp;Ying Zhang ,&nbsp;Xiaojun Xu ,&nbsp;Dong Jiang","doi":"10.1016/j.cnsns.2025.108610","DOIUrl":"10.1016/j.cnsns.2025.108610","url":null,"abstract":"<div><div>Strongly Nonlinear Energy Sink structures (NESs) have been widely developed to achieve better performance of vibration suppression recently. Utilizing nonlinear stiffness designs poses great challenges to the system's restoring force measurement and parameter identification. The SINDy (sparse identification of nonlinear dynamics) method has significantly enhanced the efficacy of parameter identification in the past decade. However, the practical considerations regarding model selection, anti-noise capability, synchronized variable retrieval, etc., still pose challenges in strongly nonlinear structure identification. The primary contribution of this study is to conduct thorough investigations on the SINDy identification of strongly NESs encompassing: 1) characterizing the types of strong nonlinearities; 2) exploring numerical techniques for integration and differentiation; 3) selecting appropriate free and forced vibration responses; 4) assessing robustness against noise interference; and 5) considering other equally important aspects. Numerical simulations are conducted on four typical NES structures including piecewise linear, hysteretic, softening-hardening and tristable types to validate these practical issues. The findings indicate that employing a numerical differentiation approach, utilizing a dataset of forced vibration, and maintaining noise levels below 30 dB can yield enhanced identification outcomes. Finally, some discussions on sparse identification of strongly nonlinear NES structures have been illustrated and potential prospects to improve identification accuracy and efficiency are summarized.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108610"},"PeriodicalIF":3.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021209","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
Weak and Wasserstein convergence of periodic measures of stochastic neural field lattice models with Heaviside ’s operators and locally Lipschitz Lévy noises 具有Heaviside算子和局部Lipschitz lsamvy噪声的随机神经场格模型周期测度的弱收敛性和Wasserstein收敛性
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-13 DOI: 10.1016/j.cnsns.2025.108602
Hailang Bai, Mingkai Yuan, Dexin Li, Yunshun Wu
{"title":"Weak and Wasserstein convergence of periodic measures of stochastic neural field lattice models with Heaviside ’s operators and locally Lipschitz Lévy noises","authors":"Hailang Bai,&nbsp;Mingkai Yuan,&nbsp;Dexin Li,&nbsp;Yunshun Wu","doi":"10.1016/j.cnsns.2025.108602","DOIUrl":"10.1016/j.cnsns.2025.108602","url":null,"abstract":"<div><div>We study the global-in-time well-posedness and periodic measures for a class neural field lattice models (with Heaviside’s operators) defined on the high-dimensional integer set <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, and driven by locally Lipschitz Lévy noises. We first formulate the stochastic neural field lattice equations into abstract stochastic systems defined in the infinite-dimensional weighted Hilbert space, and then prove the global-in-time well-posedness of the stochastic systems. When the time-dependent forces are periodic, the existence of periodic measures is obtained by the idea of uniform tail-estimates and the Krylov–Bogolyubov method. The limiting behavior of the periodic measures in the weak convergence sense is discussed as the noises intensities approach zero. A stronger convergence of the periodic measures is also established in the Wasserstein distance sense.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108602"},"PeriodicalIF":3.4,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987024","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
A closed-form solution for pricing European-style options under the Heston model with credit and liquidity risks 基于赫斯顿模型的欧式期权定价的封闭式解决方案，其中包含信用和流动性风险
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-12 DOI: 10.1016/j.cnsns.2025.108595
Xin-Jiang He , Shou-De Huang , Sha Lin
{"title":"A closed-form solution for pricing European-style options under the Heston model with credit and liquidity risks","authors":"Xin-Jiang He ,&nbsp;Shou-De Huang ,&nbsp;Sha Lin","doi":"10.1016/j.cnsns.2025.108595","DOIUrl":"10.1016/j.cnsns.2025.108595","url":null,"abstract":"<div><div>Credit risks are one type of hazardous financial risks, which results in the necessity of considering vulnerable options. Two involved assets, corresponding to underlying and option seller’s ones, both follow Heston stochastic volatility with different parameters, and their prices are discounted via a stochastic factor relying on stochastic market-wide liquidity. We then develop a general formula after the establishment of a risk-neutral measure, and it can be computed analytically since we are able to derive a closed-form joint characteristic function. Liquidity and volatility risks are shown through numerical experiments to significantly impact vulnerable option prices.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108595"},"PeriodicalIF":3.4,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143021211","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
On a matrix KdV6 equation 在矩阵KdV6方程上
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-12 DOI: 10.1016/j.cnsns.2025.108605
Pilar R. Gordoa , Andrew Pickering , Jonathan A.D. Wattis
{"title":"On a matrix KdV6 equation","authors":"Pilar R. Gordoa ,&nbsp;Andrew Pickering ,&nbsp;Jonathan A.D. Wattis","doi":"10.1016/j.cnsns.2025.108605","DOIUrl":"10.1016/j.cnsns.2025.108605","url":null,"abstract":"<div><div>The so-called KdV6 equation has, since its discovery, been the subject of much interest. In this paper we present a matrix version of this equation. On the one hand, we use the Darboux transformation to derive its Bäcklund transformation and a nonlinear superposition formula. These are then used, in the case of upper-triangular matrices, to obtain one- and two-soliton solutions. We find that wave components can combine to produce rogue waves. On the other hand, we derive a second matrix partial differential equation, for which we give auto-Bäcklund transformations of a different kind, similar to those usually given for Painlevé equations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108605"},"PeriodicalIF":3.4,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The neural network basis method for nonlinear partial differential equations and its Gauss–Newton optimizer 非线性偏微分方程的神经网络基方法及其高斯-牛顿优化器
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-11 DOI: 10.1016/j.cnsns.2025.108608
Jianguo Huang , Haohao Wu
{"title":"The neural network basis method for nonlinear partial differential equations and its Gauss–Newton optimizer","authors":"Jianguo Huang ,&nbsp;Haohao Wu","doi":"10.1016/j.cnsns.2025.108608","DOIUrl":"10.1016/j.cnsns.2025.108608","url":null,"abstract":"<div><div>This paper focuses on designing the neural network basis method (NNBM) and its optimizer for solving systems of nonlinear partial differential equations (PDEs) in two/three dimensions. We first discretize the underlying problem in terms of a set of neural network basis functions from ELM-type methods combined with the collocation method, so as to produce a nonlinear least squares method (which is named as the NNBM specifically). Then, we elaborate on the implementation procedure of the Gauss–Newton method for the previous minimization problem. Moreover, it is proved by mathematical induction that this method is equivalent to the Newton-LLSQ method proposed by Dong and Li in 2021. Further, we use the method to numerically solve two typical nonlinear PDEs in mechanics. The numerical results show the proposed method is efficient and accurate if the exact solution is sufficiently smooth.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108608"},"PeriodicalIF":3.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987023","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
Eigenfunction expansion method to characterize Rayleigh waves in nonlocal orthotropic thermoelastic medium with double porosity 双孔隙非局部正交各向异性热弹性介质中瑞利波的特征函数展开法
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-10 DOI: 10.1016/j.cnsns.2025.108599
Chandra Sekhar Mahato, Siddhartha Biswas
{"title":"Eigenfunction expansion method to characterize Rayleigh waves in nonlocal orthotropic thermoelastic medium with double porosity","authors":"Chandra Sekhar Mahato,&nbsp;Siddhartha Biswas","doi":"10.1016/j.cnsns.2025.108599","DOIUrl":"10.1016/j.cnsns.2025.108599","url":null,"abstract":"<div><div>The present manuscript addresses the Rayleigh wave propagation in a nonlocal orthotropic thermoelastic half-space with double porosity within the dual-phase-lag model of hyperbolic thermoelasticity. An eigenvalue technique is used to solve the resulting vector-matrix differential equation. Boundary conditions include stress-free, thermally insulated, and isothermal surfaces. The frequency equations of Rayleigh waves are derived in numerous scenarios. The well-known frequency equation of the Rayleigh wave in classical elasticity is derived as a particular case from the present problem. Surface particle motion during Rayleigh wave propagation is derived. Throughout the motion, elliptical surface particle paths are observed. To illustrate and validate the analytical developments, the numerical solution of frequency equations, eccentricities, and inclination of particle trajectories with wave normal are performed, and the computer-simulated results are graphically displayed. The various Rayleigh wave characteristics, such as propagation speed, attenuation coefficient, penetration depth, and specific loss against wave number, are presented graphically.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108599"},"PeriodicalIF":3.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986956","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
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