Communications in Nonlinear Science and Numerical Simulation最新文献

英文中文

A novel complexity reduction technique using visibility relationship and perpendicular distance recursive refinement for physiological signals

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-04 DOI: 10.1016/j.cnsns.2025.108752

Orhan Atila , Muhammed Halil Akpinar , Abdulkadir Sengur , U.R. Acharya

Signal simplification is a processing technique that reduces the number of samples in a signal. It has been employed in various applications and methods while handling huge amounts of data. One well-known method is the Douglas-Peucker (DP) algorithm which performs signal simplification using an appropriate tolerance value to determine whether to retain or remove a given sample point. That would mean the performance of the DP algorithm is sensitive to the selection of the tolerance value. In this paper, we introduce a new signal simplification method insensitive to parameter dependence changes. We first construct a connectivity-based visibility relationship matrix to find the most important points in the signal. Then, we use the degree threshold value to construct a degree matrix determining key anchors of the simplification process that preserve the essential features of the signal. This signal is simplified by measuring the perpendicular distances of the intermediate points from line segments defined by these key points. The proposed technique was tested on three simulated signal models and an electroencephalography (EEG) signal. Our results obtained are visually and quantitatively compared in terms of root mean square error (RMSE), R², number of simplified points, and compression ratio with the DP algorithm. The results indicate that the proposed method is robust to parameter changes and provides better simplification than the DP algorithm. In the future, we plan to validate our algorithm with a huge database.

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引用次数: 0

Evolutionary stochastic characteristics of nonlinear oscillator with one side barrier due to multiple modulated Gaussian white noise

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-03 DOI: 10.1016/j.cnsns.2025.108696

Guo-Kang Er, Jie Luo, Vai Pan Iu

In this paper, the evolutionary exponential-polynomial-closure (EPC) method is extended to study the challenging problem of obtaining the evolutionary probability density function (EPDF) solutions of the nonlinear stochastic oscillators with one barrier under multiple modulated Gaussian white noise. Firstly, the original oscillator with the barrier is transformed into a new approximately equivalent nonlinear oscillator in the state space

R^{2}

through the variable transformation. Subsequently, the presented procedure is employed to solve the non-stationary FPK equation in the transformed state space. After that, the EPDFs of the original oscillator can be acquired based on the variable transformation. To determine the accuracy of the presented procedure, three illustrative examples are investigated by considering distinct nonlinear terms, restitution factors and multiple random excitations. The accuracy of the EPDFs acquired by the presented procedure is compared with that of simulated results in each example. The outcomes illustrate that the presented procedure can provide accurate EPDF solutions and it is more efficient than numerical simulation. The EPDF solutions of the oscillator are greatly affected by the barrier, the correlation of the noise and the modulation function in the system. The asymmetry of EPDFs can also be influenced significantly by the barrier and the correlation of the modulated noise. In the evolving process, the statistical moments of responses also vary in a similar trend as the modulated function of the white noise due to the barrier.

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引用次数: 0

Reinforcement learning for adaptive time-stepping in the chaotic gravitational three-body problem

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-03 DOI: 10.1016/j.cnsns.2025.108723

Veronica Saz Ulibarrena, Simon Portegies Zwart

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

{"title":"Reinforcement learning for adaptive time-stepping in the chaotic gravitational three-body problem","authors":"Veronica Saz Ulibarrena, Simon Portegies Zwart","doi":"10.1016/j.cnsns.2025.108723","DOIUrl":"10.1016/j.cnsns.2025.108723","url":null,"abstract":"<div><div>Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108723"},"PeriodicalIF":3.4,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550953","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

Effects of a moving barrier on the first-passage time of a diffusing particle under stochastic resetting

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-03 DOI: 10.1016/j.cnsns.2025.108732

Telles Timóteo Da Silva

We study a first-passage time problem for a one-dimensional diffusion under stochastic resetting through a moving barrier described by a piecewise affine function. It is shown that the mean first-passage time can be minimized with respect to the resetting rate. However, the mean first-passage time exhibits multiple extrema as a function of the resetting rate, depending on the choice of the model parameters. This contrasts with the diffusion with stochastic resetting with static barrier, where only a single minimum exists. We develop a detailed numerical example in the case where the moving barrier is an alternating sequence of a constant function and an affine function with arbitrary slope. It is found that the optimal resetting rate varies discontinuously with the slope.

引用次数: 0

Construction and analysis for orthonormalized Runge–Kutta schemes of high-index saddle dynamics

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-01 DOI: 10.1016/j.cnsns.2025.108731

Shuai Miao , Lei Zhang , Pingwen Zhang , Xiangcheng Zheng

Saddle points are prevalent in complex systems and contain important information. The high-index saddle dynamics (HiSD) and the generalized HiSD (GHiSD) are two efficient approaches for determining saddle points of any index and for constructing the solution landscape. In this work, we first present an example to show that the orthonormality of directional vectors in saddle dynamics is critical in locating the saddle point. Then we construct two orthonormalized Runge–Kutta schemes tailored for the HiSD and GHiSD. We find that if a set of vectors are almost orthonormal with the error

O (τ^{α})

for some

α > 0

, then the Gram–Schmidt process also applies an

O (τ^{α})

perturbation to orthonormalize them. We apply this and employ the structures of Runge–Kutta schemes to prove the almost orthonormality in numerical schemes and then prove their second-order accuracy with respect to the time step size. We substantiate the theoretical findings by several numerical experiments.

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引用次数: 0

Global exponential stability of periodic solutions for inertial delayed BAM neural networks

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-01 DOI: 10.1016/j.cnsns.2025.108728

Wentao Wang , Wei Zeng , Wei Chen

In this paper, we utilize the characteristic method to establish new sufficient conditions for the global exponential stability of periodic solutions for inertial delayed bidirectional associative memory (BAM) neural networks. The proposed criteria are presented as a series of linear scalar inequalities, which notably circumvent the use of the reduced order method and Lyapunov–Krasovskii functionals (LKFs), distinguishing them from prior results and offering simple solvability. Finally, we corroborate the analytical findings through three numerical examples supported by their corresponding simulations.

引用次数: 0

Consistency-enhanced E-SAV BDF2 time-marching method with relaxation for the hydrodynamically-coupled binary phase-field crystal model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation

Pub Date : 2025-03-01 DOI: 10.1016/j.cnsns.2025.108730

Jingwen Wu , Xin Zhang , Yanyao Wu , Zhijun Tan

This paper focuses on the hydrodynamically-coupled binary phase-field crystal (BPFC) model. Based on the

L^{2}

-gradient flow, we derive the governing equations from the energy functional. To ensure the conservation of total mass, we incorporate two nonlocal Lagrange multipliers. For fluid dynamics, we employ the incompressible Navier–Stokes (NS) equations. Subsequently, we analytically prove the crucial property of energy dissipation within the model. To devise the numerical scheme, we reformulate the governing equations into an equivalent representation by incorporating an exponential scalar auxiliary variable (E-SAV). By leveraging the second-order backward difference formula (BDF2), we initially devise a second-order scheme and subsequently correct the energy through a relaxation technique applied to the E-SAV, with the objective of enhancing energy consistency. At every time step, due to the complete decoupling of variables, we solve only a limited number of elliptic equations to update the relevant variables. Furthermore, we analyze the unique solvability and energy stability of the time-discretized method. To confirm the performance of our proposed scheme, we perform various numerical experiments aimed at validating its effectiveness, accuracy, and stability.

{"title":"Consistency-enhanced E-SAV BDF2 time-marching method with relaxation for the hydrodynamically-coupled binary phase-field crystal model","authors":"Jingwen Wu , Xin Zhang , Yanyao Wu , Zhijun Tan","doi":"10.1016/j.cnsns.2025.108730","DOIUrl":"10.1016/j.cnsns.2025.108730","url":null,"abstract":"<div><div>This paper focuses on the hydrodynamically-coupled binary phase-field crystal (BPFC) model. Based on the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-gradient flow, we derive the governing equations from the energy functional. To ensure the conservation of total mass, we incorporate two nonlocal Lagrange multipliers. For fluid dynamics, we employ the incompressible Navier–Stokes (NS) equations. Subsequently, we analytically prove the crucial property of energy dissipation within the model. To devise the numerical scheme, we reformulate the governing equations into an equivalent representation by incorporating an exponential scalar auxiliary variable (E-SAV). By leveraging the second-order backward difference formula (BDF2), we initially devise a second-order scheme and subsequently correct the energy through a relaxation technique applied to the E-SAV, with the objective of enhancing energy consistency. At every time step, due to the complete decoupling of variables, we solve only a limited number of elliptic equations to update the relevant variables. Furthermore, we analyze the unique solvability and energy stability of the time-discretized method. To confirm the performance of our proposed scheme, we perform various numerical experiments aimed at validating its effectiveness, accuracy, and stability.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108730"},"PeriodicalIF":3.4,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143550966","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

Phase shifts inside Arnold tongues of weakly coupled oscillators

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.2025.108729

Jakub Záthurecký, Veronika Eclerová, Jan Ševčík, Štěpán Zapadlo, Lenka Přibylová

In this paper, we investigate phase synchronization phenomena in weakly coupled oscillators, with a particular focus on the phase shifts that occur within Arnold tongues. Using a proposed theoretical approach, we provide proof of the existence of the corresponding cycle manifold near zero coupling, along with a detailed derivation of its shape. This allows us to explore the conditions under which phase-shift synchronization arises. We employ the implicit function theorem in an appropriate Banach space to establish the existence of the cycle manifold and provide a methodology to study in-phase and anti-phase synchrony in systems governed by both ordinary and delay differential equations. We introduce a numerical technique for cycle continuation that reveals the shift structure of Arnold tongues in coupling and parameter space near the cusps, offering new insights into the dynamics of phase-shifted coupled oscillators. This framework is applied to a classic model of two coupled circle oscillators, coupled van der Pol oscillators, a model of two interneurons, and a two-level interneuronal network to better understand and demonstrate the numerical continuation methodology, which allows for the study of phase synchronization in neuroscience and other fields. The proposed methods not only advance the theoretical understanding of synchronization but also offer practical computational tools for studying complex oscillatory systems.

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引用次数: 0

Stability and error analysis of linear IMEX schemes for sixth-order Cahn–Hilliard-type equations

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.2025.108724

Nan Zheng , Jie Shen

In this paper, we develop efficient implicit-explicit (IMEX) schemes for solving sixth-order Cahn–Hilliard-type equations based on the generalized scalar auxiliary variable (GSAV) approach. These novel schemes provide several remarkable advantages: (i) they are linear and only require solving one elliptic equation with constant coefficients at each time step; (ii) they are unconditionally energy stable and yield a uniform bound for the numerical solution. We also establish rigorous error estimates of up to fifth-order for these schemes, and present various numerical experiments to validate the stability and accuracy of the proposed schemes.

引用次数: 0

Event-triggered based composite observer-oriented quantized truncated predictive tracking control for Markovian jump delay systems

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.2025.108727

N. Shobana , Ardashir Mohammadzadeh , N. Wongvanich , R. Sakthivel

This study encapsulates the multifaceted nature of attaining precise state tracking objectives in Markovian jump delay systems by encompassing a control technique related to delay compensation, fault tolerance, disturbance suppression and mismatch quantization. In brief, a quantized truncated predictive tracking control technique is implemented to achieve enhanced tracking outcomes by attenuating the influence of time-delays and mismatch quantization. Additionally, as a means of preventing transmission burden in the observer channel, an event-triggering-based composite generalized extended state observer is formulated to offer concurrent evaluations of plant states, actuator faults and external disturbances to the control device. Altogether, an event-triggered composite generalized extended state observer-oriented quantized truncated predictive tracking control algorithm is proposed with the objective of obtaining preferential tracking results despite the detrimental aspects. Specifically, by implying delay-dependent Lyapunov–Krasovskii functionals, we delineate the necessities for ensuring the stochastic stability of the specified system, detailed by linear matrix inequalities. Furthermore, the credibility of the examined findings is affirmed through graphical plots of numerical simulations.

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引用次数: 0

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Communications in Nonlinear Science and Numerical Simulation

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