Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

Exponential synchronization of chaotic Lur’e systems with observer-based aperiodic time-triggered intermittent control

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-28 DOI: 10.1016/j.cnsns.2025.108726

Han Wang , Qingzhi Wang , Baozeng Fu , Lijie Wang

In this paper, observer-based aperiodic time-triggered intermittent control (OATIC) is introduced to study the exponential synchronization of chaotic Lur’e systems (CLSs). Firstly, the operation principle of CLSs with OATIC is elaborated in detail. Based on it, the mathematical expression of OATIC is proposed. Secondly, with the aid of the deduced lemma and the constructed mixed time-dependent Lyapunov functional (MTLF), sufficient conditions are derived to ensure the exponential stability of the augmented system. Thirdly, by congruent transformation, matrix decomposition and linear matrix inequality techniques, the exponential synchronization theorem is established for CLSs with OATIC. As a result, OATIC is designed. Compared with sampled-data control (SC), time-triggered intermittent control (TIC) and aperiodic time-triggered intermittent control (ATIC), OATIC is superior to them in function. Finally, a simulation example is provided for verification.

引用次数: 0

Delayed state-feedback control for synchronization of complex networks with coupling delays and impulsive disturbances

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-28 DOI: 10.1016/j.cnsns.2025.108700

Youzhi Dong, Xiuping Han, Xiaodi Li

This paper concentrates on the synchronization problem of complex networks subject to coupling delays and impulsive disturbances, employing delayed state-feedback control strategies. By constructing a Lyapunov–Krasovskii functional with two different exponential decay rates, the complex networks with impulsive disturbances can achieve globally exponential synchronization (GES). Furthermore, the derived synchronization norms establish a link between coupling delay and feedback delay. This paper considers the normal situation in which the control term is expressed as

B_{i} u_{i}

, where

B_{i}

is a common

n \times m

real matrix. Tackling this type of issue poses greater challenges than dealing with the special case where

B_{i}

is an identity matrix. Through appropriate selection of matrix

B_{i}

, the controller can be effectively employed across all or certain states. To demonstrate the practical validity of the proposed approach, a numerical example is presented to illustrate its effectiveness.

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引用次数: 0

Error estimates of a SAV-BDF2 finite element method with variable time steps for the Cahn–Hilliard–Navier–Stokes phase-field model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-27 DOI: 10.1016/j.cnsns.2025.108718

Danxia Wang , Jiongzhuo Lv , Yanping Chen

In this work, an efficient fully discrete numerical scheme is presented for the Cahn–Hilliard–Navier–Stokes phase-field model. The combination of the variable time step second-order backward difference formula (VBDF2) and the finite element method is applied for discretization in time and space. Simultaneously, the scalar auxiliary variable (SAV) approach is employed to deal with the nonlinear term. Firstly, the unique solvability, mass conservation, and stability of the SAV-VBDF2 finite element scheme are proved. Secondly, the error estimates are provided through rigorous analysis. Additionally, an adaptive time step strategy is designed to enhance the computational efficiency while guaranteeing the accuracy. Finally, some numerical simulations are conducted to verify the previous analysis results.

引用次数: 0

Special function-based limited-time synchronization of multilayered coupled quaternion networks

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-27 DOI: 10.1016/j.cnsns.2025.108694

Kailong Xiong , Cheng Hu , Juan Yu , Leimin Wang

In this article, the stability problem for nonlinear systems and the synchronization of multilayered coupled quaternion networks involving memristor are separately discussed within a limited time, the time here can be determined by system or control parameters, or it can be specified by actual demand. To start with, based on exponential and hyperbolic cosine function, the theorems for limited-time stability are developed by virtue of inequality techniques and reduction to absurdity, which are distinct from the power-law function-based conditions and more concise in the estimate of the convergence time. Besides, a general form of multi-layer quaternion-valued delayed coupled neural network model is proposed, several exponential and hyperbolic cosine function control protocols are designed in the quaternion field to achieve limited-time synchronization, which are different from the existing power-law control design and the complicated decomposition-based results. To conclude, three examples are provided to demonstrate the validity of the established results.

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引用次数: 0

On convergence analysis of feedback control with integral action and discontinuous relay perturbation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-27 DOI: 10.1016/j.cnsns.2025.108698

Michael Ruderman

We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with discontinuous Coulomb-type friction. We recall the stiction region is globally attractive where the resulting hybrid system has also solutions in Filippov sense, while the motion trajectories remain in that idle state (called in tribology as stiction) until the formulated sliding-mode condition is violated by the growing integral feedback quantity. We analyze the conditions for occurrence of the slowly converging stick–slip cycles. We also show that the hybrid system is globally but only asymptotically stable, and almost always not exponentially. A particular case of the exponential convergence can appear for some initial values, assuming the characteristic equation of the linear subsystem has dominant real roots. Illustrative numerical examples are provided alongside with the developed analysis. In addition, a laboratory example is shown with experimental evidence to support the convergence analysis provided.

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引用次数: 0

Extreme events suppression in a suspended aircraft seat system under extreme environment

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-27 DOI: 10.1016/j.cnsns.2025.108707

Dan Zhao , Yongge Li , Qi Liu , Jürgen Kurths , Yong Xu

In extreme flight environments, extreme oscillations may occur in aircraft seats, seriously endangering passengers’ comfort and safety. It is important to quantitatively study extreme events in the aircraft seats and control them. In this paper, a two-degree-of-freedom suspended seat is used to describe aircraft seats and a nonlinear energy sink (NES) is employed to suppress extreme events. The extreme flight environments are characterized by non-Gaussian Lévy noise. We discover extreme events by observing the system responses and the probability density functions. By investigating the relationship between seat and attachment and the effect of Lévy noise on extreme events, the quantification of extreme events is achieved. Furthermore, the mechanism by which NES fulfills extreme event suppression is explored. The mean first-passage time and the probability of extreme events are calculated, and the impacts of NES parameters on the performance of extreme events suppression are performed. The results indicate that, damping and linear stiffness coefficients help extreme events suppression. These findings contribute to improving the theoretical guidance for designing such systems.

{"title":"Extreme events suppression in a suspended aircraft seat system under extreme environment","authors":"Dan Zhao , Yongge Li , Qi Liu , Jürgen Kurths , Yong Xu","doi":"10.1016/j.cnsns.2025.108707","DOIUrl":"10.1016/j.cnsns.2025.108707","url":null,"abstract":"<div><div>In extreme flight environments, extreme oscillations may occur in aircraft seats, seriously endangering passengers’ comfort and safety. It is important to quantitatively study extreme events in the aircraft seats and control them. In this paper, a two-degree-of-freedom suspended seat is used to describe aircraft seats and a nonlinear energy sink (NES) is employed to suppress extreme events. The extreme flight environments are characterized by non-Gaussian Lévy noise. We discover extreme events by observing the system responses and the probability density functions. By investigating the relationship between seat and attachment and the effect of Lévy noise on extreme events, the quantification of extreme events is achieved. Furthermore, the mechanism by which NES fulfills extreme event suppression is explored. The mean first-passage time and the probability of extreme events are calculated, and the impacts of NES parameters on the performance of extreme events suppression are performed. The results indicate that, damping and linear stiffness coefficients help extreme events suppression. These findings contribute to improving the theoretical guidance for designing such systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108707"},"PeriodicalIF":3.4,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550965","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

High-order fractional central difference method for multi-dimensional integral fractional Laplacian and its applications

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-27 DOI: 10.1016/j.cnsns.2025.108711

Huanfeng Yang , Hongbin Chen , Xiaoqiang Yue , Guangqing Long

In order to change the current situation where the numerical accuracy of existing fractional central difference (FCD) methods for integral fractional Laplacian (IFL) does not exceed second-order no matter how smooth the solution is. A simple and easy-to-implement high-order FCD scheme on uniform meshes is proposed for multi-dimensional IFL. The new generating functions are constructed to accommodate the discretization of the classical and integral fractional Laplacian in a unified framework. Compared to other finite difference methods, the weights or coefficients of high-order FCD can be easily calculated using fast Fourier transform (FFT). And our scheme inherits the merits of the existing FCD method, such as the FFT efficiency and low storage costs. Furthermore, it can be extended to arbitrary bounded domains via the fictitious domain method, which allow the FFT algorithm. The stability and convergence analysis of our method are given in solving the fractional Poisson equations. Extensive numerical experiments are provided to verify our theoretical results. The new method can even achieve eighth order accuracy when the solution is sufficiently smooth. Utilizing its efficiency, our method is applied to solve the time-dependent problems with IFL that included of fractional Schrödinger equation, fractional Allen–Cahn equation and anomalous diffusion problems, some new observations are discovered from our numerical simulations.

{"title":"High-order fractional central difference method for multi-dimensional integral fractional Laplacian and its applications","authors":"Huanfeng Yang , Hongbin Chen , Xiaoqiang Yue , Guangqing Long","doi":"10.1016/j.cnsns.2025.108711","DOIUrl":"10.1016/j.cnsns.2025.108711","url":null,"abstract":"<div><div>In order to change the current situation where the numerical accuracy of existing fractional central difference (FCD) methods for integral fractional Laplacian (IFL) does not exceed second-order no matter how smooth the solution is. A simple and easy-to-implement high-order FCD scheme on uniform meshes is proposed for multi-dimensional IFL. The new generating functions are constructed to accommodate the discretization of the classical and integral fractional Laplacian in a unified framework. Compared to other finite difference methods, the weights or coefficients of high-order FCD can be easily calculated using fast Fourier transform (FFT). And our scheme inherits the merits of the existing FCD method, such as the FFT efficiency and low storage costs. Furthermore, it can be extended to arbitrary bounded domains via the fictitious domain method, which allow the FFT algorithm. The stability and convergence analysis of our method are given in solving the fractional Poisson equations. Extensive numerical experiments are provided to verify our theoretical results. The new method can even achieve eighth order accuracy when the solution is sufficiently smooth. Utilizing its efficiency, our method is applied to solve the time-dependent problems with IFL that included of fractional Schrödinger equation, fractional Allen–Cahn equation and anomalous diffusion problems, some new observations are discovered from our numerical simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108711"},"PeriodicalIF":3.4,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511923","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

Dual-robust divergence-free and efficiently decoupled scheme for three-dimensional thermally coupled magnetohydrodynamic systems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-26 DOI: 10.1016/j.cnsns.2025.108725

Zeyu Xie, Haiyan Su, Xinlong Feng

In this paper, a structure-preserving (for both

\nabla \cdot u_{h}^{n + 1} = 0

and

\nabla \cdot B_{h}^{n + 1} = 0

), unconditionally stable and decoupled scheme is proposed for the three-dimensional (3D) thermally coupled magnetohydrodynamic (MHD) model. Firstly, the thermally coupled MHD model is rewritten using the Lamb identity, and the variable vorticity is introduced to avoid

\nabla u

existing. Secondly, the mixed finite element method is employed for spatial discretization, where the velocity and magnetic field are discretized by the

H (div, Ω)

-conforming face element. It is worth note that, the velocity and magnetic field only need to use the lowest order Raviart–Thomas face element, so that the velocity and magnetic field are divergence-free at the discrete level. The first-order semi-implicit Euler method is used for time discretization. And then, a first-order stabilization term is added to ensure the unconditional stability and the decoupling of the velocity and magnetic field for the desired scheme. At each time step, only four subproblems need to be solved. Furthermore, we also provides a rigorous proof of the unique solvability and unconditional stability of the proposed scheme. Finally, the effectiveness of the scheme is verified by numerical examples.

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引用次数: 0

Stabilization of nonlinear Timoshenko system just with local damping and local coupling effects acting on arbitrarily chosen subintervals

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-26 DOI: 10.1016/j.cnsns.2025.108721

Kun-Peng Jin , Jin Liang , Ti-Jun Xiao

We are concerned with the stabilization of nonlinear Timoshenko system just with local damping and local coupling effects, which come from the local memory/frictional terms and local coupling terms, acting on arbitrarily chosen subintervals. Especially, the subintervals do not necessarily include the ends and intersect each other, unlike what is usually required. For this challenging problem, we successfully establish a stability theorem with the exact uniform decay rates for the solutions to this system with the help of some specially designed analysis approaches for the problem. Also, polynomial/exponential decay rates are obtained, when the memory kernels decay polynomially/exponentially. Our results reveal an important phenomenon that for the nonlinear Timoshenko system, local coupling and damping effects are enough to produce an entire dissipation mechanism as those for the case of the global coupling and damping effects, and the same decay rates can be obtained. Moreover, under quite weak conditions on the memory kernels, our stability theorem gives stronger conclusions than the previous corresponding results, whether global or local memory effect is concerned.

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引用次数: 0

Stability of stochastic time-varying delay continuous system uniting event trigger switching control

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-02-26 DOI: 10.1016/j.cnsns.2025.108703

Zhenyue Wang , Quanxin Zhu

The main objective of this article is to discuss the problem of finite-time stochastic input-to-state stability for a kind of stochastic delay continuous system with time-varying delay. By applying Lyapunov-Razumikhin functions as candidate functions, several sufficient criteria to ensure system stability are established. Different from the content of previous achievements, the event trigger switching control is investigated in the switching behavior among subsystems in this article. Further, the Zeno phenomenon is ruled out, that is, the gap between any adjacent switching points should be greater than a positive constant. Compared with the time trigger switching control, the advantage of the event trigger switching control is that the target system undergoes switching behavior when the event trigger conditions are satisfied. Moreover, the delay factor of continuous subsystems is contained within event trigger conditions to determine the switching time. Finally, two numerical simulations are displayed to validate our results.

引用次数: 0

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