Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Dynamics of a diffusive model in the anaerobic digestion process","authors":"Lin Wang, Linlin Bu, Jianhua Wu","doi":"10.1016/j.cnsns.2024.108523","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108523","url":null,"abstract":"The joined effects of syntrophic relationship and substrate inhibition are considered in a diffusive model of the anaerobic digestion process. We first establish the existence and structure of coexistence solutions for the system in different growth rate parameter ranges. Numerical results suggest that the coexistence solutions of the system undergo double bifurcation in the suitable range of growth rate coefficients. The time evolution of solutions simulated in a high-dimensional space further demonstrates the multiplicity, as well as the magnitude and the spatial distribution of solutions for the system, offering valuable insights for future theoretical analysis. The effect of substrate inhibition on species coexistence is analyzed, and the result reveals that species cannot coexist when the substrate inhibition is sufficiently large. Finally, the dynamic behavior of the system is investigated from both theoretical and numerical perspectives, including the global attractivity of semi-trivial steady-state solutions and the uniform persistence of the system.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"23 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849252","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}

{"title":"Small noise and small time asymptotics for McKean–Vlasov SDEs with local Lipschitz coefficients","authors":"Jinming Li, Wei Liu, Yi Sun, Luhan Yang","doi":"10.1016/j.cnsns.2024.108535","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108535","url":null,"abstract":"This work is mainly concerned with small noise and small time asymptotics for a class of McKean–Vlasov stochastic differential equations with local Lipschitz coefficients. We apply the modified weak convergence criteria to prove the Laplace principle (equivalently, the large deviation principle). The main results extend the existing ones to the case of fully local assumptions with respect to both the state and measure variables in the literature. As a consequence, the small time asymptotics for McKean–Vlasov SDEs are also derived.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"25 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886871","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}

{"title":"A novel active learning method based on the anisotropic kernel density estimation for global metamodeling in support of engineering design","authors":"Jiaxing Wang, Wei Zhao, Xiaoping Wang, Yangyang Chen, Xueyan Li","doi":"10.1016/j.cnsns.2024.108530","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108530","url":null,"abstract":"In modern engineering practice, there is a steady increase in the need for multi-dimensional global approximations of complex black-box functions involved in today's engineering design problems. Metamodels have been proved to be effective alternatives for analyzing and predicting highly complex original models at a lower computational cost. The Kriging model is valued for its ability to predict the uncertainty of unknown points, which makes it widely used in the active learning methods for global approximation. However, these methods do not extend well to other metamodeling methods. This paper proposes an anisotropic kernel density estimation-based global fit (AKDGF) criterion for the active learning of metamodel. The AKDGF consists of two terms: global exploration dependent on the anisotropic kernel density (AKD) estimation and local development for larger nonlinear regions, which can be combined with various metamodeling methods. The initial sample set should be uniformly distributed in the design space as evenly as possible. Therefore, the uniform design approach is utilized to select the initial sample set for building the metamodel, and the AKDGF selects samples with high expected improvements to the metamodel to update the DOE sequentially. Five numerical examples and three engineering examples are presented to illustrate the proposed method and prove its good performance.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"14 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849251","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}

{"title":"An efficient spectral method for two-dimensional Fredholm integro-differential equations in complex geometries","authors":"Hanwen Wang, Guoqing Yao, Zicheng Wang","doi":"10.1016/j.cnsns.2024.108526","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108526","url":null,"abstract":"Classical spectral methods are confined to numerically solving Fredholm integro-differential equations in regular domains, such as rectangles and discs. This paper aims to numerically address two-dimensional Fredholm integro-differential equations in complex geometries by combining spectral methods with mapping techniques. Initially, we transform the computational domain into a rectangular one via coordinate mapping. Subsequently, classical spectral methods are applied within this rectangular domain for numerical simulations. Our analysis primarily discusses the existence, uniqueness and convergence of numerical solutions. Numerical results demonstrate that the proposed method achieves high-order accuracy.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"262 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849253","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}

{"title":"A delay decomposition method for uncertain T–S fuzzy systems with stochastic time-delay under switching event-triggered control","authors":"Ling He, Congfeng Jiang, Liangbin Zhang","doi":"10.1016/j.cnsns.2024.108519","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108519","url":null,"abstract":"This study seeks to achieve exponential stabilization of uncertain Takagi–Sugeno (T–S) fuzzy systems with stochastic time-varying delays using a switching event-triggered <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control strategy. A delay decomposition scheme is used to build a time-dependent piecewise Lyapunov function and stability criteria are established using reciprocally convex and integral inequalities. A switched event-triggered mechanism is utilized to determine the moments of triggering, and a matrix decoupling method is used to propose a co-design strategy for both feedback gains and event-trigger matrices. Finally, the effectiveness and superiority of the proposed delay decomposition method are thoroughly verified by simulations involving a numerical example and a model of a truck-trailer system.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"41 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886875","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}

{"title":"A coupled model of information-epidemic considering heterogeneity in individual activity levels in multiple networks","authors":"Xiaoxiao Xie, Liang'an Huo, Yingying Cheng","doi":"10.1016/j.cnsns.2024.108552","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108552","url":null,"abstract":"Studying the intrinsic mechanisms of coupled information and epidemic transmission can enhance public understanding of the dynamic processes involved in epidemic transmission. Heterogeneous individual activity levels reshape propagation mechanisms, influencing the co-evolutionary dynamics of information and epidemics. We developed a novel coupled information-epidemic model to investigate how variations in individual activity levels affect the dynamic propagation process. This model differs from previous ones by incorporating individual activity heterogeneity, which reshapes linking mechanisms between nodes, affecting the mechanisms of information diffusion, epidemic transmission, and inter-layer social reinforcement. Using a micro-Markov chain approach (MMCA), we deduced the outbreak threshold. Our study revealed the following key findings: (i) individual activity levels in the epidemic transmission layer have a more significant effect on epidemic transmission; (ii) inter-layer social reinforcement can inhibit epidemic transmission; (iii) the stronger the local information influence—indicated by a higher proportion of individuals aware of surrounding information—accelerates information diffusion, thereby inhibiting epidemic transmission; and (iv) enhancing the influence of information on epidemics can further inhibit epidemic transmission. The complexity of these coupled interactions emphasizes the importance of individual behaviors in the dynamics of the entire social system, providing a theoretical foundation for developing effective prevention strategies.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886874","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}

{"title":"Stability and chemical modeling of quantifying disparities in atmospheric analysis with sustainable fractal fractional approach","authors":"Muhammad Farman, Changjin Xu, Perwasha Abbas, Aceng Sambas, Faisal Sultan, Kottakkaran Sooppy Nisar","doi":"10.1016/j.cnsns.2024.108525","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108525","url":null,"abstract":"Fractional-order derivative-based modeling is crucial for describing real-world forecasting problems and analyzing proposed models. It provides an advanced framework for examining intricate variations in various systems, enhancing understanding and analysis. We present a new fractional order nonlinear model for dynamics and forecasting of nitrogen oxides <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mtext>NO</mml:mtext></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math> and ozone <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mtext>O</mml:mtext></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math> in the atmosphere, crucial for air quality regulation and smog formation. The study compares invariant regions and solution pathways within complex reaction mechanisms impacting the ozone layer. The study uses Banach’s contraction theorem, Schauder’s fixed-point theorem, and fixed-point theory to study a proposed model. Fundamental equations are studied, and local sensitivity analysis is performed using MATLAB’s Sim-Biology toolbox. The model is stabilized using the linear feedback regulate method, considering a fractional-order system with a managed design. Moment quintile regression is used to validate coefficient parameters for forecasting and modeling. Theoretical predictions are validated using the two-step Newton Polynomial Method, and numerical results show high agreement between theoretical analysis and numerical results. The research introduces a new method for quantifying invariant curve disparities using advanced Model Reduction Techniques (MRTs), focusing on the proximity between model predictions and actual data points. The method identifies achievable invariant regions and influential parameters for <mml:math altimg=\"si3.svg\" display=\"inline\"><mml:mrow><mml:mtext>NO</mml:mtext><mml:mi>x</mml:mi></mml:mrow></mml:math> and <mml:math altimg=\"si4.svg\" display=\"inline\"><mml:msub><mml:mrow><mml:mtext>O</mml:mtext></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> under environmental stressors. Results validate theoretical and experimental findings by employing local as well as non-singular kernels at various fractional order values and fractal dimensions to show the strong memory effect.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"53 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849255","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}

{"title":"Bayesian autoregressive online change-point detection with time-varying parameters","authors":"Ioanna-Yvonni Tsaknaki, Fabrizio Lillo, Piero Mazzarisi","doi":"10.1016/j.cnsns.2024.108500","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108500","url":null,"abstract":"Change points in real-world systems mark significant regime shifts in system dynamics, possibly triggered by exogenous or endogenous factors. These points define regimes for the time evolution of the system and are crucial for understanding transitions in financial, economic, social, environmental, and technological contexts. Building upon the Bayesian approach introduced in Adams and MacKay (2007), we devise a new method for online change point detection in the mean of a univariate time series, which is well suited for real-time applications and is able to handle the general temporal patterns displayed by data in many empirical contexts. We first describe time series as an autoregressive process of an arbitrary order. Second, the variance and correlation of the data are allowed to vary within each regime driven by a scoring rule that updates the value of the parameters for a better fit of the observations. Finally, a change point is detected in a probabilistic framework via the posterior distribution of the current regime length. By modeling temporal dependencies and time-varying parameters, the proposed approach enhances both the estimate accuracy and the forecasting power. Empirical validations using various datasets demonstrate the method’s effectiveness in capturing memory and dynamic patterns, offering deeper insights into the non-stationary dynamics of real-world systems.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"48 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886877","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}

{"title":"Prediction of the flutter envelope and parametric analysis of a flutter-based aeroelastic piezoelectric energy harvester","authors":"Ying Hao, Jinghan Li","doi":"10.1016/j.cnsns.2024.108520","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108520","url":null,"abstract":"This is a comprehensive study on a 2-degree-of-freedom flutter-based aeroelastic piezoelectric energy harvester supported with cubic and quintic nonlinear springs under unsteady airflow. The nonlinear system is simplified by dimension reduction analysis for a high-dimensional multistable system, and the flutter envelope is predicted and the parameters studied to analyze the effect on linear critical flutter velocity and output power. Then, the probability density function is obtained by stochastic averaging, and the influences of airflow disturbance intensity and nonlinear parameters on the most probable response and energy harvesting efficiency are analyzed. Appropriate disturbance intensity reduces flutter speed while increasing amplitude in the plunge direction and output voltage. However, excessive disturbance diminishes energy collection efficiency and may cause system failure.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"202 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886876","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}

{"title":"Balanced implicit two-step Maruyama methods for stochastic differential equations","authors":"Quanwei Ren, Jiayi Liu, Yanyan He","doi":"10.1016/j.cnsns.2024.108512","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108512","url":null,"abstract":"This paper introduces balanced implicit two-step Maruyama methods for solving Itô stochastic differential equations. Such methods, compared to those corresponding standard linear two-step Maruyama methods, have better mean-square properties, which is confirmed by a comparison of the stability regions for some particular two-step Maruyama methods. Moreover, the convergence order is investigated which proves the convergence of the presented methods with the order <mml:math altimg=\"si298.svg\" display=\"inline\"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math> in the mean-square sense. Numerical results are reported to show the convergence properties and the stability properties of the balanced implicit two-step Maruyama methods. The stability analysis and numerical results show that the proposed methods are very promising methods for stiff stochastic differential equations.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849491","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}