Communications in Nonlinear Science and Numerical Simulation最新文献

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Dynamics of the 2-D quadratic family: Coexistence of strange attractors 二维二次族动力学:奇异吸引子的共存
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108877
A. Marqués-Lobeiras, A. Pumariño, J.Á. Rodríguez, E. Vigil
{"title":"Dynamics of the 2-D quadratic family: Coexistence of strange attractors","authors":"A. Marqués-Lobeiras,&nbsp;A. Pumariño,&nbsp;J.Á. Rodríguez,&nbsp;E. Vigil","doi":"10.1016/j.cnsns.2025.108877","DOIUrl":"10.1016/j.cnsns.2025.108877","url":null,"abstract":"<div><div>This paper deals with the dynamics of the quadratic two-parameter family <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>x</mi><mo>+</mo><mi>b</mi><mi>y</mi><mo>)</mo></mrow></mrow></math></span> that arises as the limit family in generic unfoldings of homoclinic tangencies in the 3-D diffeomorphism scenario. In particular, the coexistence of persistent (strange) attractors is shown.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108877"},"PeriodicalIF":3.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936251","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
Radial basis function interpolation-multiscale optimized dual-threshold permutation entropy and its application to mechanical fault diagnosis 径向基函数插值-多尺度优化双阈值排列熵及其在机械故障诊断中的应用
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108904
Yuxing Li, Qiyu Ding, Yingmin Yi, Yiwei Yuan
{"title":"Radial basis function interpolation-multiscale optimized dual-threshold permutation entropy and its application to mechanical fault diagnosis","authors":"Yuxing Li,&nbsp;Qiyu Ding,&nbsp;Yingmin Yi,&nbsp;Yiwei Yuan","doi":"10.1016/j.cnsns.2025.108904","DOIUrl":"10.1016/j.cnsns.2025.108904","url":null,"abstract":"<div><div>Permutation entropy (PE) and multiscale PE (MPE) are effective methods for measuring the complexity of nonlinear signals and have been widely utilized in mechanical fault diagnosis. However, PE neglects the specific differences of amplitude and MPE suffers from information loss at larger scales. To address the limitation of PE, dual-threshold permutation entropy (DPE) is proposed, which exactly characterizes the complexity of nonlinear signals by precise division of permutation patterns to fully take into account the specific differences of amplitude through introducing the double thresholds. Furthermore, optimized DPE (ODPE) is developed to solve the threshold selection issues of DPE and thus improve applicability. To address the issue of MPE, radial basis function interpolation-multiscale ODPE (RIMODPE) is introduced as a multiscale extension of ODPE, which compensate for the loss of information on large scales by employing interpolation-multiscale techniques to supplement more information points. The four sets of synthetic signal experiments verify that compared to permutation entropy, dispersion entropy, sample entropy and fuzzy entropy, ODPE has excellent sensitiveness and robustness, and RIMODPE has superior separability and stability. Two sets of real-signal experiments reveal that mechanical fault diagnosis accuracy of RIMODPE both exceeds 97%, and it maintains reliable performance in diagnosing mechanical faults even with limited sample, which indicates that RIMODPE is well-suited for practical industrial machinery fault diagnosis.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108904"},"PeriodicalIF":3.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143886539","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
Highly efficient and accurate numerical schemes for the anisotropic phase field crystal models by using the improved scalar auxiliary variable (iSAV) approach 利用改进的标量辅助变量(iSAV)方法求解各向异性相场晶体模型的高效、精确的数值格式
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108875
Xiaoli Wang, Zhengguang Liu
{"title":"Highly efficient and accurate numerical schemes for the anisotropic phase field crystal models by using the improved scalar auxiliary variable (iSAV) approach","authors":"Xiaoli Wang,&nbsp;Zhengguang Liu","doi":"10.1016/j.cnsns.2025.108875","DOIUrl":"10.1016/j.cnsns.2025.108875","url":null,"abstract":"<div><div>The two-dimensional anisotropic phase field crystal (APFC) model is a sixth-order nonlinear parabolic equation that can be used to simulate various phenomena such as epitaxial growth, material hardness, and phase transition. The scalar auxiliary variable method (SAV) is a common method to solve various nonlinear dissipative systems, and the improved SAV (iSAV) method is not only completely linear, but also strictly guarantees the original dissipation law. In this paper, we construct several efficient, accurate linear and original energy-stable numerical schemes of the APFC model based on the iSAV method. Firstly, a first-order iSAV scheme is considered to keep the original energy stability for the APFC model. Secondly, we propose a new stabilized iSAV scheme and give its rigorous energy stability analysis to keep its original dissipation law. Finally, several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108875"},"PeriodicalIF":3.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873737","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
Discrete natural logarithmic barrier function-based prescribed performance backstepping control for MEMS resonator 基于离散自然对数势垒函数的MEMS谐振器规定性能反步控制
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108910
Le Zhao, Guanci Yang, Yang Li, Kexin Luo, Junxing Zhang, Ling He
{"title":"Discrete natural logarithmic barrier function-based prescribed performance backstepping control for MEMS resonator","authors":"Le Zhao,&nbsp;Guanci Yang,&nbsp;Yang Li,&nbsp;Kexin Luo,&nbsp;Junxing Zhang,&nbsp;Ling He","doi":"10.1016/j.cnsns.2025.108910","DOIUrl":"10.1016/j.cnsns.2025.108910","url":null,"abstract":"<div><div>The prescribed performance control is able to optimize both the transient and static performance of the controlled object by pre-set performance indicators, thereby ensuring that the output error remains within a predetermined small range despite any interference or uncertainty within the system. Considering this, aiming at the discrete micro-electromechanical system (MEMS) resonator, we design a discrete natural logarithmic barrier function-based prescribed performance backstepping controller. Among them, firstly, the discrete interval type-3 fuzzy logic system (IT3FLS) and discrete tracking differentiator are constructed to approximate the virtual control input and unknown nonlinear function. Secondly, a prescribed performance adaptive fuzzy backstepping controller based on the constructed discrete natural logarithmic barrier function is designed to constrain the output errors of the system, and enhance transient and static performances of the controller. Then, a discrete event-triggered mechanism based on the switch threshold is constructed and integrated into the designed controller to release unnecessary resource occupation and controller computational burden on the premise of ensuring tracking accuracy. Furthermore, through the mean-square stability criterion, we demonstrate that all signals of this system are exponentially mean-square stable, and tracking errors fall within the prescribed constraint region. Finally, simulation and comparative experiment results display that the designed controller performs well in the transient performance, static performance and robustness.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108910"},"PeriodicalIF":3.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895539","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
Convergence and applications of novel FISTA-like algorithms 新型类fista算法的收敛与应用
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI: 10.1016/j.cnsns.2025.108871
Yeyu Zhang , Hongwei Liu , Yan Tang
{"title":"Convergence and applications of novel FISTA-like algorithms","authors":"Yeyu Zhang ,&nbsp;Hongwei Liu ,&nbsp;Yan Tang","doi":"10.1016/j.cnsns.2025.108871","DOIUrl":"10.1016/j.cnsns.2025.108871","url":null,"abstract":"<div><div>In this paper, a novel unified framework of fast iterative shrinkage-thresholding algorithm (FISTA)-like algorithms is proposed for nonsmooth convex minimization problems in real Hilbert spaces, which includes several variants (e.g., forward–backward splitting methods, inertial forward–backward algorithms, and FISTA). The convergence rates of the objective function and the iterative algorithm are studied, and the strong convergence is obtained provided that the objective function is uniformly convex. Secondly, a perturbed version of the FISTA-like algorithms is presented. Two strategies for the selection of the step size and improvement measures for the local oscillation behavior of the algorithm are introduced, which greatly improves the practical application performance. In addition, the model of the continuous dynamical system is established, and also the asymptotic property is obtained. Finally, the effectiveness and superiority of the proposed algorithms are verified by LASSO problems, image deblurring, and signal recovery.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108871"},"PeriodicalIF":3.4,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881430","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
Homogeneous nonlinear event-triggered extended state observers for uncertain MIMO random systems 不确定MIMO随机系统的齐次非线性事件触发扩展状态观测器
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-23 DOI: 10.1016/j.cnsns.2025.108827
Zijian Xiao, Xiaohua Liu, Ze-Hao Wu, Pengyu Zeng, Zhongwen Liang
{"title":"Homogeneous nonlinear event-triggered extended state observers for uncertain MIMO random systems","authors":"Zijian Xiao,&nbsp;Xiaohua Liu,&nbsp;Ze-Hao Wu,&nbsp;Pengyu Zeng,&nbsp;Zhongwen Liang","doi":"10.1016/j.cnsns.2025.108827","DOIUrl":"10.1016/j.cnsns.2025.108827","url":null,"abstract":"<div><div>In this paper, homogeneous nonlinear event-triggered extended state observers (ESOs) constructed from finite-time stable systems are designed for a class of uncertain multi-input multi-output (MIMO) random systems. Each subsystem is subject to the nonlinear coupling effect of nonlinear unmodeled dynamics, bounded noise, and colored noise, which is regarded as the random total disturbance. An event generator with a guaranteed positive minimum inter-execution time for every sample path solution of the random systems, is developed for the design of homogeneous nonlinear event-triggered ESO for each subsystem. The almost sure convergence of estimation errors of unmeasurable states and random total disturbance of each subsystem is demonstrated with a rigorous theoretical proof. Some numerical simulations are provided to authenticate the theoretical result.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108827"},"PeriodicalIF":3.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868312","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 of spiral wave chimeras subjected to a local feedback control 局部反馈控制下螺旋波嵌合体的动力学
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-23 DOI: 10.1016/j.cnsns.2025.108859
Yaqi Xue, Guoyong Yuan, Feng Guo, Wenrui Shen
{"title":"Dynamics of spiral wave chimeras subjected to a local feedback control","authors":"Yaqi Xue,&nbsp;Guoyong Yuan,&nbsp;Feng Guo,&nbsp;Wenrui Shen","doi":"10.1016/j.cnsns.2025.108859","DOIUrl":"10.1016/j.cnsns.2025.108859","url":null,"abstract":"<div><div>The response of the spiral wave chimera on the feedback signal from a measuring location is investigated in the three-component reaction–diffusion system with two spatial dimensions. When the feedback gain is small, the feedback forces the incoherent core to follow a circular orbit with finger-shaped bulges, and the circular path exhibits more complex structures with an increases of the time delay. For a large feedback gain, the excitation in front of the wave front causes the disappearance of the spiral arm except for some residual segments, which will be developed into the wave structures with multiple incoherent cores, where one of the cores is located at the measuring point. Four types of dynamical behaviors are identified for an intermediate feedback gain, depending on the time delay, and these behaviors cannot be observed in the local feedback control of normal spiral waves. For the first three types, the spiral chimera will eventually disappear, but through three different processes, including the formation of transient incoherent arcs, the drift of the incoherent core to the boundary along a spiral, and the complex drift with a transient closed path. The fourth type appears for a large time delay, where the incoherent core drifts to the measuring point along a spiral. These results relate to the control of the spiral chimera, where the spiral chimera can be eliminated by the feedback exhibiting the first three dynamical behaviors, and its core can be controlled to the designated location by the feedback exhibiting the fourth dynamical behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108859"},"PeriodicalIF":3.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881429","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
Physical insights from complex multiscale non-linear system dynamics: Identification of fast and slow variables 复杂多尺度非线性系统动力学的物理洞察:快速和慢速变量的识别
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-23 DOI: 10.1016/j.cnsns.2025.108858
Dimitris M. Manias , Ronald N. Goldman , Dimitris A. Goussis
{"title":"Physical insights from complex multiscale non-linear system dynamics: Identification of fast and slow variables","authors":"Dimitris M. Manias ,&nbsp;Ronald N. Goldman ,&nbsp;Dimitris A. Goussis","doi":"10.1016/j.cnsns.2025.108858","DOIUrl":"10.1016/j.cnsns.2025.108858","url":null,"abstract":"<div><div>There are many applications governed by nonlinear dynamical systems in which the model is introduced in a standard (natural) basis of a vector space, but it is more natural to analyze this model using a different set of basis vectors, which is more suitable for the acquisition of the relevant physical insights. Here the case of multiscale dynamical systems is considered, for which the appropriate alternative set of basis vectors is the one resolving the tangent space. Simple algorithmic tools are introduced that identify the fast and slow variables, thus facilitating (i) the construction of reduced models and (ii) the design of novel pathways for controlling complex multiscale systems across diverse scientific disciplines. The usefulness of these tools is demonstrated in two well-known multiscale models: the Michaelis–Menten and the Lorenz models.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108858"},"PeriodicalIF":3.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903428","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
Three implementations of B-differentiable Newton method in solving 3D elastoplastic frictional contact problems and their discussion b -可微牛顿法求解三维弹塑性摩擦接触问题的三种实现及其讨论
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-22 DOI: 10.1016/j.cnsns.2025.108888
Hangduo Gao , Zhiqiang Hu , Zhao Yin , Gao Lin
{"title":"Three implementations of B-differentiable Newton method in solving 3D elastoplastic frictional contact problems and their discussion","authors":"Hangduo Gao ,&nbsp;Zhiqiang Hu ,&nbsp;Zhao Yin ,&nbsp;Gao Lin","doi":"10.1016/j.cnsns.2025.108888","DOIUrl":"10.1016/j.cnsns.2025.108888","url":null,"abstract":"<div><div>In this paper, three implementations of B-differentiable Newton method (BDNM) for solving 3D elastoplastic frictional contact problems are presented. In the first two methods, a nested strategy is employed. The contact equations, which are solely associated with the contact conditions in the normal and tangential directions due to the introduction of the contact flexibility matrix, are expressed as B-differentiable equations. They are solved in the external iteration, or regarded as a sub-step nested within the solution of nonlinear equilibrium equations, leading to the decoupling of the calculations for nonlinear equilibrium equations and contact forces. In the third method, both the nonlinear equilibrium equations and contact conditions are expressed as B-differentiable equations simultaneously. Both nodal displacement and contact force are treated as independent variables, solved using BDNM to ensure the global convergence, with a variant of a Jacobian matrix associated with unknowns derived. In the numerical examples, the accuracy of the proposed methods is demonstrated by comparing with the results obtained from ANSYS. The convergence and computational efficiency are investigated through a series of models with varying degrees of freedom (DOFs) and contact node pairs (CNPs). The robustness of the proposed methods is presented by applying them to the analysis of an arch dam with seven transverse joints.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108888"},"PeriodicalIF":3.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873736","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
Calculating SIRD model parameters and Re-susceptibility in Malaysia, Pakistan, India and United Arab Emirates 计算马来西亚、巴基斯坦、印度和阿拉伯联合酋长国的SIRD模式参数和再敏感性
IF 3.4 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-22 DOI: 10.1016/j.cnsns.2025.108902
Abdul Basit , Jasni Mohamad Zain , Hafiza Zoya Mojahid , Abdul Kadir Jumaat , Nur’Izzati Hamdan , Dilip Kumar Bagal
{"title":"Calculating SIRD model parameters and Re-susceptibility in Malaysia, Pakistan, India and United Arab Emirates","authors":"Abdul Basit ,&nbsp;Jasni Mohamad Zain ,&nbsp;Hafiza Zoya Mojahid ,&nbsp;Abdul Kadir Jumaat ,&nbsp;Nur’Izzati Hamdan ,&nbsp;Dilip Kumar Bagal","doi":"10.1016/j.cnsns.2025.108902","DOIUrl":"10.1016/j.cnsns.2025.108902","url":null,"abstract":"<div><div>During the dynamic spread of COVID-19 and the looming threat of future pandemics the essential need of precise epidemiological models are indispensable. Key to these algorithms are the estimation of core parameters a pivotal metric indicating pandemic expansion. Yet, existing algorithms often overlook crucial facets such as viral mutations risks. Addressing this gap, we propose an innovative algorithm merging the Susceptible-Infected-Recovered-Dead (SIRD) model with <em>Re</em>-susceptible compartment incorporated by least square method with linear regression approach that ensures the accurate parameter estimation facilitating real-time forecasting. This idea analyzed different countries full lockdown scenario. These incorporation of statistical and mathematical algorithms enhances parameters estimation, forecasting and provides insights into re-susceptibility percentage. The experiments revealed convincing results with the incorporation of statistical and mathematical algorithms enhancing parameter estimation with best R-square values of 0.9902 for country Pakistan exemplifying its vital contribution to pandemic response strategies. Our work offers a vital tool for governments, institutions and individuals grappling with pandemic responded full lockdown policy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"148 ","pages":"Article 108902"},"PeriodicalIF":3.4,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143881431","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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