Pub Date : 2025-01-10DOI: 10.1016/j.cnsns.2025.108604
Jiyu Zhu, Qikun Shen
This article focuses on the distributed fault-tolerant control (FTC) problem for a class of interconnected nonlinear systems with unknown higher powers. In order to reduce the excessive resource consumption and address the denial-of-service (DoS) attacks, an event-triggered communication mechanism (ECM) with multiple DoS detectors is developed for interconnected nonlinear systems for the first time, especially unknown higher powers are included, instead of strictly equal to one as in the relevant results. Besides, unlike the previous works where only actuator faults are considered, the FTC strategy proposed in this article can handle communication component failures as well. Then, an adaptive neural controller is constructed by utilizing back-stepping technique and the tracking error of each subsystem is proven to converge to a small neighborhood of the origin even in the present of DoS attacks based on Lyapunov stability theory. Finally, the developed strategy is applied to a class of coupled inverted pendulum (CIP) systems and the simulation result demonstrates the validity.
{"title":"A novel distributed neural FTC strategy for interconnected nonlinear systems with unknown higher powers and its applications to CIPs","authors":"Jiyu Zhu, Qikun Shen","doi":"10.1016/j.cnsns.2025.108604","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108604","url":null,"abstract":"This article focuses on the distributed fault-tolerant control (FTC) problem for a class of interconnected nonlinear systems with unknown higher powers. In order to reduce the excessive resource consumption and address the denial-of-service (DoS) attacks, an event-triggered communication mechanism (ECM) with multiple DoS detectors is developed for interconnected nonlinear systems for the first time, especially unknown higher powers are included, instead of strictly equal to one as in the relevant results. Besides, unlike the previous works where only actuator faults are considered, the FTC strategy proposed in this article can handle communication component failures as well. Then, an adaptive neural controller is constructed by utilizing back-stepping technique and the tracking error of each subsystem is proven to converge to a small neighborhood of the origin even in the present of DoS attacks based on Lyapunov stability theory. Finally, the developed strategy is applied to a class of coupled inverted pendulum (CIP) systems and the simulation result demonstrates the validity.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"2 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986955","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}
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman–Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees m(m≥1) and m−1 respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree m to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and L2 norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results.
本文开发并分析了一类针对非稳态不可压缩对流布林克曼-福克海默方程的半离散和全离散弱 Galerkin 有限元方法。在空间离散化方面，这些方法分别采用度数为 m（m≥1）和 m-1 的分片多项式来逼近元素内部的速度和压力，并采用度数为 m 的分片多项式来逼近元素界面上的数值迹线。在完全离散方法中，使用后向欧拉差分方案来近似时间导数。结果表明，这些方法可以得到全局无发散的速度近似值。建立了能量规范和 L2 规范的最佳先验误差估计。设计了一种收敛线性化迭代算法，用于求解完全离散系统。提供了数值实验来验证理论结果。
{"title":"Robust globally divergence-free weak Galerkin methods for unsteady incompressible convective Brinkman–Forchheimer equations","authors":"Xiaojuan Wang, Jihong Xiao, Xiaoping Xie, Shiquan Zhang","doi":"10.1016/j.cnsns.2024.108578","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108578","url":null,"abstract":"This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman–Forchheimer equations. For the spatial discretization, the methods adopt the piecewise polynomials of degrees <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi>m</mml:mi><mml:mspace width=\"1em\"></mml:mspace><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> and <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mi>m</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> respectively to approximate the velocity and pressure inside the elements, and piecewise polynomials of degree <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mi>m</mml:mi></mml:math> to approximate their numerical traces on the interfaces of elements. In the fully discrete method, the backward Euler difference scheme is used to approximate the time derivative. The methods are shown to yield globally divergence-free velocity approximation. Optimal a priori error estimates in the energy norm and <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> norm are established. A convergent linearized iterative algorithm is designed for solving the fully discrete system. Numerical experiments are provided to verify the theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"54 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986959","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}
Pub Date : 2025-01-09DOI: 10.1016/j.cnsns.2025.108590
Elena Braverman, Cemil Tunç, Osman Tunç
A system with, generally, unbounded and non-continuous delays is considered as a perturbation of a linear non-delay system. Boundedness of solutions, stability, global asymptotic stability, uniform exponential stability are established with a variety of methods, including designing a Lyapunov–Krasovskii functional and integral transformations. The system incorporates a linear non-delay part and a sum of either linear or nonlinear terms, dependent on several time-variable delays. The dependency of the stability type on the delay properties is outlined and illustrated with examples.
{"title":"On global stability of nonlinear systems with unbounded and distributed delays and a dominating non-delay term","authors":"Elena Braverman, Cemil Tunç, Osman Tunç","doi":"10.1016/j.cnsns.2025.108590","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108590","url":null,"abstract":"A system with, generally, unbounded and non-continuous delays is considered as a perturbation of a linear non-delay system. Boundedness of solutions, stability, global asymptotic stability, uniform exponential stability are established with a variety of methods, including designing a Lyapunov–Krasovskii functional and integral transformations. The system incorporates a linear non-delay part and a sum of either linear or nonlinear terms, dependent on several time-variable delays. The dependency of the stability type on the delay properties is outlined and illustrated with examples.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"34 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986960","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}
Pub Date : 2025-01-07DOI: 10.1016/j.cnsns.2025.108597
Yuxing Li, Yilan Lou, Chunli Zhang
Link dispersion entropy (LDE), as an improvement of dispersion entropy (DE), focuses on transition states between adjacent dispersion patterns. However, the transition states of dispersion patterns at different intervals are ignored and parameters of LDE have a significant impact on entropy value. To address these problems, grayscale dispersion entropy (GDE) is proposed, which introduces transition step size considering the transition states between dispersion patterns at different intervals, reflecting the state transition information comprehensively and uses a grayscale matrix instead of a transition probability matrix to weaken the effect of parameter on entropy value. Moreover, multiscale grayscale dispersion entropy (MGDE) is proposed as a multiscale version of GDE, which reflects the complexity at various time scales. Simulation experiments have confirmed that GDE possesses the capability to precisely detect dynamic changes in signal and accurately represent signal complexity. For two types of publicly available ship radiated noise datasets and rolling bearing dataset, MGDE has better classification performance than other four complexity metrics.
链接色散熵（LDE）是对色散熵（DE）的改进，主要关注相邻色散模式之间的过渡状态。然而，不同间隔的色散模式的过渡状态被忽视，而且 LDE 的参数对熵值有很大影响。针对这些问题，提出了灰度色散熵（GDE），它引入了考虑不同间隔色散模式之间过渡状态的过渡步长，全面反映了状态过渡信息，并使用灰度矩阵代替过渡概率矩阵，削弱了参数对熵值的影响。此外，还提出了多尺度灰度色散熵（MGDE），作为 GDE 的多尺度版本，它反映了不同时间尺度上的复杂性。模拟实验证实，GDE 具有精确检测信号动态变化的能力，并能准确表示信号的复杂性。对于两种公开的船舶辐射噪声数据集和滚动轴承数据集，MGDE 比其他四种复杂度指标具有更好的分类性能。
{"title":"Multiscale grayscale dispersion entropy: A new nonlinear dynamics metric for time series analysis","authors":"Yuxing Li, Yilan Lou, Chunli Zhang","doi":"10.1016/j.cnsns.2025.108597","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108597","url":null,"abstract":"Link dispersion entropy (LDE), as an improvement of dispersion entropy (DE), focuses on transition states between adjacent dispersion patterns. However, the transition states of dispersion patterns at different intervals are ignored and parameters of LDE have a significant impact on entropy value. To address these problems, grayscale dispersion entropy (GDE) is proposed, which introduces transition step size considering the transition states between dispersion patterns at different intervals, reflecting the state transition information comprehensively and uses a grayscale matrix instead of a transition probability matrix to weaken the effect of parameter on entropy value. Moreover, multiscale grayscale dispersion entropy (MGDE) is proposed as a multiscale version of GDE, which reflects the complexity at various time scales. Simulation experiments have confirmed that GDE possesses the capability to precisely detect dynamic changes in signal and accurately represent signal complexity. For two types of publicly available ship radiated noise datasets and rolling bearing dataset, MGDE has better classification performance than other four complexity metrics.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"205 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986963","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}
Pub Date : 2025-01-07DOI: 10.1016/j.cnsns.2025.108591
Yutao Yan, Shuzhen Yu, Zhiyong Yu, Haijun Jiang, Hui Wang
Taking into account the phenomenon of cross-platform propagation of network information and multi-platform network environments, this paper constructs two discrete-time negative information propagation models with time delays. For the single platform model, we first prove that the information-free equilibrium (IFE) is locally asymptotically stable (LA-stable) and globally asymptotically stable (GA-stable) when ℛ0<1. Then, by using the method of Lyapunov function, it is obtained that when ℛ0>1, the information-spreading equilibrium (ISE) is GA-stable. For the multi-platform model, it is found that its dynamic behaviors are completely determined by the propagation threshold ℜˆ0. To be specific, the IFE of the multi-platform model is GA-stable when ℜˆ0<1. With respect to ℜˆ0>1, it is proved that the ISE is GA-stable by using graph theory approach. The numerical experiments verify the accuracy of the conclusions. In the end, a real case is selected to illustrate the applicability of the model.
{"title":"Global dynamics of delayed discrete-time SEIR negative information propagation model with multi-platform and cross-transmission mechanism","authors":"Yutao Yan, Shuzhen Yu, Zhiyong Yu, Haijun Jiang, Hui Wang","doi":"10.1016/j.cnsns.2025.108591","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108591","url":null,"abstract":"Taking into account the phenomenon of cross-platform propagation of network information and multi-platform network environments, this paper constructs two discrete-time negative information propagation models with time delays. For the single platform model, we first prove that the information-free equilibrium (IFE) is locally asymptotically stable (LA-stable) and globally asymptotically stable (GA-stable) when <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\"><</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>. Then, by using the method of Lyapunov function, it is obtained that when <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>, the information-spreading equilibrium (ISE) is GA-stable. For the multi-platform model, it is found that its dynamic behaviors are completely determined by the propagation threshold <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mo>ˆ</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>. To be specific, the IFE of the multi-platform model is GA-stable when <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mo>ˆ</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\"><</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>. With respect to <mml:math altimg=\"si5.svg\" display=\"inline\"><mml:mrow><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mo>ˆ</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>, it is proved that the ISE is GA-stable by using graph theory approach. The numerical experiments verify the accuracy of the conclusions. In the end, a real case is selected to illustrate the applicability of the model.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"7 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986961","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}
Pub Date : 2025-01-07DOI: 10.1016/j.cnsns.2025.108601
Bohdan Datsko, Vasyl Gafiychuk
The stability of a two-component time-fractional reaction-diffusion system during its linear stage is analyzed, revealing the emergence of a new type of instability at specific values of the fractional derivative order. With this instability, perturbations with finite wave numbers become unstable and cause spatially inhomogeneous oscillations. A comprehensive spectral study identified such type of instability across a broad range of wave numbers and system parameters. An increase in the fractional derivative order allows larger nonhomogeneous wave numbers to be linked with these unstable modes, which can trigger nonlinear nonhomogeneous oscillations and the formation of spatial oscillatory structures. The results of the linear stability analysis are confirmed by computer simulations of the fractional sub-hyperbolic Bonhoeffer-van der Pol-type reaction-diffusion system. It has been established that oscillatory-wave instability occurs also in hyperbolic systems and covers, in this limiting case, both the maximum range of wave numbers and system parameters.
分析了双组分时间-分数阶反应扩散系统在线性阶段的稳定性，揭示了在分数阶导数的特定值处出现的一种新的不稳定性。由于这种不稳定性，具有有限波数的扰动变得不稳定并引起空间非均匀振荡。一项全面的光谱研究发现，这种类型的不稳定性跨越了广泛的波数和系统参数。分数阶导数阶数的增加允许更大的非均匀波数与这些不稳定模态相关联，这可以触发非线性非均匀振荡和空间振荡结构的形成。通过对分数次双曲型Bonhoeffer-van der pol型反应扩散体系的计算机模拟，验证了线性稳定性分析的结果。已经确定振荡波不稳定性也发生在双曲系统中，并且在这种极限情况下，包括波数和系统参数的最大范围。
{"title":"Oscillatory wave bifurcation and spatiotemporal patterns in fractional subhyperbolic reaction-diffusion systems","authors":"Bohdan Datsko, Vasyl Gafiychuk","doi":"10.1016/j.cnsns.2025.108601","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108601","url":null,"abstract":"The stability of a two-component time-fractional reaction-diffusion system during its linear stage is analyzed, revealing the emergence of a new type of instability at specific values of the fractional derivative order. With this instability, perturbations with finite wave numbers become unstable and cause spatially inhomogeneous oscillations. A comprehensive spectral study identified such type of instability across a broad range of wave numbers and system parameters. An increase in the fractional derivative order allows larger nonhomogeneous wave numbers to be linked with these unstable modes, which can trigger nonlinear nonhomogeneous oscillations and the formation of spatial oscillatory structures. The results of the linear stability analysis are confirmed by computer simulations of the fractional sub-hyperbolic Bonhoeffer-van der Pol-type reaction-diffusion system. It has been established that oscillatory-wave instability occurs also in hyperbolic systems and covers, in this limiting case, both the maximum range of wave numbers and system parameters.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"29 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986962","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}
Pub Date : 2025-01-06DOI: 10.1016/j.cnsns.2025.108593
Xiaotian Hu
We investigate the long time behavior of the viscosity solution for the evolutionary contact Hamilton–Jacobi equation with state constraints. Our analysis reveals that the viscosity solution uniformly converges to a viscosity solution of the corresponding stationary contact Hamilton–Jacobi equation with state constraints as time goes to infinity.
{"title":"The asymptotic problem on contact Hamilton–Jacobi equations with state constraints","authors":"Xiaotian Hu","doi":"10.1016/j.cnsns.2025.108593","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108593","url":null,"abstract":"We investigate the long time behavior of the viscosity solution for the evolutionary contact Hamilton–Jacobi equation with state constraints. Our analysis reveals that the viscosity solution uniformly converges to a viscosity solution of the corresponding stationary contact Hamilton–Jacobi equation with state constraints as time goes to infinity.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"41 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986964","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}
Pub Date : 2025-01-04DOI: 10.1016/j.cnsns.2024.108563
Shaoxuan Chen, Panayotis G. Kevrekidis, Hong-Kun Zhang, Wei Zhu
In an earlier work by a subset of the present authors W. Zhu et al. (2023), the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi–Pasta–Ulam–Tsingou lattice and the Calogero-Moser system.
{"title":"Data-driven discovery of conservation laws from trajectories via neural deflation","authors":"Shaoxuan Chen, Panayotis G. Kevrekidis, Hong-Kun Zhang, Wei Zhu","doi":"10.1016/j.cnsns.2024.108563","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108563","url":null,"abstract":"In an earlier work by a subset of the present authors W. Zhu et al. (2023), the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we extend by a significant step this proposal. Instead of using the explicit knowledge of the underlying equations of motion, we develop the method directly from system trajectories. This is crucial towards enhancing the practical implementation of the method in scenarios where solely data reflecting discrete snapshots of the system are available. We showcase the results of the method and the number of associated conservation laws obtained in a diverse range of examples including 1D and 2D harmonic oscillators, the Toda lattice, the Fermi–Pasta–Ulam–Tsingou lattice and the Calogero-Moser system.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986965","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}
Pub Date : 2025-01-04DOI: 10.1016/j.cnsns.2025.108592
Liyuan Wang, Dongxu Cao, Jiayang Gu
This study focuses on analyzing the behavior of a graphene platelet reinforced metal foams (GPRMF) cylindrical shell under both harmonic and random excitation using advanced stochastic methods. A nonlinear stochastic differential equation describes the shell's random vibration, and the probability density function (PDF) of the vibration response is calculated using the random integral approach. The methodology demonstrates high accuracy in capturing the system's dynamic properties. The impact of external excitation frequency on the marginal and joint PDFs is thoroughly examined. The study shows that external excitation frequency significantly impacts the marginal and joint probability density functions of the vibration response. By utilizing the amplitude response curve under pure harmonic excitation, the stochastic vibration behavior under combined harmonic and white noise excitations can be effectively predicted. The study further explores the effects of random excitation strength and other parameters on the vibration response, providing insights into the displacement response and its statistical characteristics. The results validate the methods employed and highlight their capability in accurately predicting the complex dynamic behavior of GPRMF cylindrical shells.
{"title":"Nonlinear stochastic vibration of GPRMF cylindrical shell with harmonic and white noise excitations","authors":"Liyuan Wang, Dongxu Cao, Jiayang Gu","doi":"10.1016/j.cnsns.2025.108592","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.108592","url":null,"abstract":"This study focuses on analyzing the behavior of a graphene platelet reinforced metal foams (GPRMF) cylindrical shell under both harmonic and random excitation using advanced stochastic methods. A nonlinear stochastic differential equation describes the shell's random vibration, and the probability density function (PDF) of the vibration response is calculated using the random integral approach. The methodology demonstrates high accuracy in capturing the system's dynamic properties. The impact of external excitation frequency on the marginal and joint PDFs is thoroughly examined. The study shows that external excitation frequency significantly impacts the marginal and joint probability density functions of the vibration response. By utilizing the amplitude response curve under pure harmonic excitation, the stochastic vibration behavior under combined harmonic and white noise excitations can be effectively predicted. The study further explores the effects of random excitation strength and other parameters on the vibration response, providing insights into the displacement response and its statistical characteristics. The results validate the methods employed and highlight their capability in accurately predicting the complex dynamic behavior of GPRMF cylindrical shells.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"69 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986966","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}
Pub Date : 2025-01-03DOI: 10.1016/j.cnsns.2024.108587
Jingjing You, Abudujelil Abudurahman, Shuxin Liu
This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system to converge to a specific region within ST T, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practical fixed-time stability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.
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