Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Paradoxical responses of neuronal bursting to inhibitory and excitatory memristor: Different bifurcations and competitions between nonlinear and linear parts of synaptic current","authors":"Xianjun Wang ,&nbsp;Han Wang ,&nbsp;Huaguang Gu ,&nbsp;Yanbing Jia ,&nbsp;Yuye Li","doi":"10.1016/j.cnsns.2025.109086","DOIUrl":"10.1016/j.cnsns.2025.109086","url":null,"abstract":"<div><div>The complex nonlinear dynamics of neuronal firing activity modulated by the memristor exhibits important significance. In the present paper, the paradoxical responses of bursting activity induced by memristors, the corresponding nonlinear mechanisms, and roles of memristor current, are investigated in a theoretical model. Firstly, for the inhibitory memristor, increasing the gain of the memristor paradoxically widens the burst for a large transfer coefficient, whereas plays a common role to shorten the burst for small coefficient. For the excitatory memristor, only the paradoxical phenomenon of the shortened burst appears. Secondly, the common and paradoxical responses are well explained with one- and two-parameter bifurcations. The different changes of locations of saddle node bifurcation to begin the burst and homoclinic bifurcation to terminate the burst are obtained. Finally, the competition/cooperation mechanism between the nonlinear part (dependent on transfer coefficient) and linear part (independent of transfer coefficient) of the memristor current is identified, presenting the essential reason underlying the paradoxical and common bursting responses. For the inhibitory memristor, large transfer coefficient induces strong nonlinear part to override the suppressed role of the linear part, enhancing the bursting activity. Conversely, small transfer coefficient causes weak nonlinear part, overwhelmed by the suppressed effect of linear part, then, suppressed bursting appears. For the excitatory memristor, both nonlinear and linear part exhibits a suppressed role, resulting in suppression of bursting activity. These findings provide insights into the paradoxical behaviors of inhibitory and excitatory memristors and their potential functions in modulating neuronal bursting behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109086"},"PeriodicalIF":3.4,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503987","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":"Patterns of burned area by a cellular-automata fire simulator: The role of microscale wind field","authors":"A. Sahila, A. Fiorese, N. Perello, A. Trucchia, G. Pagnini","doi":"10.1016/j.cnsns.2025.109026","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109026","url":null,"abstract":"Wildfire dynamics simulated using PROPAGATOR, a quasi-empirical cellular automaton model, is studied by investigating the effects of wind-terrain interactions on the predicted burned area patterns. In order to do so, PROPAGATOR is coupled with WindNinja, a microscale wind simulator that computes spatially varying wind fields by a solver accounting for the conservation of mass and a second one assuming also conservation of momentum. Two historical fires are considered: the first one occurred in quasi-flat terrain in the Molise region of Italy, while the second ignited in the southern area of Avinyo in Spain. The standard fire simulator incorporating solely uniform wind fields and that coupled with the solvers of WindNinja predict similar burning probability maps for the Campomarino fire. The quasi-flatness of the Campomarino terrain is the main cause since the wind pattern is very weakly affected by its topography during fire propagation, resulting in only a slight deviation from the initial uniform wind field. However, in the presence of the complex topography of the Avinyo region, the fire spread simulations incorporating the spatially-varying wind fields predict significantly different burned area shapes for long time regimes and intense winds, where secondary fire spots separated from the main burning zone emerge. Larger spatial extension of the wildfire is observed in the absence of firefighters’ actions, but the predicted patterns seem to be similar regardless of the type of wind field input and its resolution. A 10-fold increase of perturbation magnitude on wind direction yields a contraction of the predicted burned area for all the probability thresholds considered, while a 2-fold and 10-fold increase of the wind speed perturbations lead to a significantly larger burned area and fire spread. Further quantitative analysis of the importance of incorporating spatially-varying wind fields in improving the predictability of cellular automata models in the case of megafires is mandatory.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"18 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503814","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":"Phase-field modeling of fiber-based thermal diffusion and phase transitions in the fused deposition modeling process","authors":"Binhu Xia ,&nbsp;Sijing Lai ,&nbsp;Qing Xia ,&nbsp;Xiang Liu ,&nbsp;Yibao Li ,&nbsp;Junseok Kim","doi":"10.1016/j.cnsns.2025.109071","DOIUrl":"10.1016/j.cnsns.2025.109071","url":null,"abstract":"<div><div>This paper introduces an advanced phase-field equation designed to accurately simulate solid–liquid phase transitions and thermal transport during the fused deposition modeling procedure. The model incorporates bidirectional coupling between phase transitions and thermal diffusion, which allows for precise predictions of temperature distribution and detailed tracking of phase evolution influenced by temperature changes. Additionally, it dynamically accounts for the moving heat source in fused deposition modeling by integrating a temperature field that evolves with nozzle movement. To further enhance heat transfer accuracy, a heat convection term combined with the nozzle velocity field is introduced. The proposed algorithm ensures consistency between the digital simulation environment and real-world physical quantities. This consistency provides a highly realistic representation of the fused deposition modeling process. This approach enables effective simulation of temperature distribution and the resulting changes in the geometry and structure of printed parts. It also supports the prediction and optimization of part quality and output in additive manufacturing.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109071"},"PeriodicalIF":3.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501383","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 improved stochastic method for conducting system probabilistic analysis by solving FPK equations","authors":"Guo-Kang Er ,&nbsp;Guo-Peng Bai ,&nbsp;Huanping Li ,&nbsp;Vai Pan Iu ,&nbsp;Chi Chiu Lam","doi":"10.1016/j.cnsns.2025.109083","DOIUrl":"10.1016/j.cnsns.2025.109083","url":null,"abstract":"<div><div>This paper proposes an improved stochastic approach to solve the Fokker–Planck–Kolmogorov (FPK) equation for conducting system probabilistic analysis. The FPK equations, associated with the system under random excitation, are solved to provide the probabilistic solutions, which are essential for system reliability analysis. The proposed method is developed based on the optimization-oriented exponential-polynomial-closure (OEPC) method, and enhances OEPC by ensuring the limitation property of the probabilistic solution, named ’improved OEPC’ method. The key innovation of this study lies in introducing constraints for undetermined parameters to ensure the limitation property of the probabilistic solution. The limitation property means that the solution of FPK approaches zero as the state variables in FPK approach infinity. This improvement guarantees the solution accuracy across a wider spatial range when dealing with rare events, such as system failures of mechanical structures. The methodology is verified by investigating three different types of system: the Duffing oscillator, the ship rolling system, and the wind-excited frame tower system. The results show that the improved OEPC method significantly enhances the tail behavior of the probabilistic solution for complex nonlinear stochastic systems compared to the conventional OEPC method. Additionally, the improved OEPC method outperforms the Gaussian closure method in terms of solution accuracy and demonstrates considerably higher efficiency compared to Monte Carlo simulation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109083"},"PeriodicalIF":3.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503968","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":"Parameter analysis in continuous data assimilation for various turbulence models","authors":"Débora A.F. Albanez, Maicon José Benvenutti, Samuel Little, Jing Tian","doi":"10.1016/j.cnsns.2025.109073","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109073","url":null,"abstract":"In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier–Stokes-<mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mi mathvariant=\"normal\">α</mml:mi></mml:math> model. Rigorous estimates are presented for the convergence of continuous data assimilation methods when the parameters of the turbulence models are not known a priori. Our approach involves creating an approximate solution for the turbulence models by employing an interpolant operator based on the observational data of the systems. The estimation depends on the parameter alpha in the models. Additionally, numerical simulations are presented to validate our theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"103 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503967","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":"Advancing solutions of integer and fractional order system of PDE’s using a modified transform method","authors":"Abd Ullah ,&nbsp;Aman Ullah ,&nbsp;Walid Emam ,&nbsp;Zeeshan Ali ,&nbsp;Dragan Pamucar ,&nbsp;Subhan Ullah","doi":"10.1016/j.cnsns.2025.109088","DOIUrl":"10.1016/j.cnsns.2025.109088","url":null,"abstract":"<div><div>Systems of partial differential equations (PDEs) serve as fundamental tools for modeling and solving complex, multidimensional problems involving interdependent processes. This paper introduces an efficient technique for solving linear and nonlinear systems of PDEs of both integer and fractional orders. The proposed method, referred to as the Modified Yang Transform Method (MYT), combines the Adomian Decomposition Method with the Yang Transform. Owing to its simplicity and versatility, this approach holds significant potential for application across diverse scientific and engineering fields. A generalized solution procedure is outlined in a step-by-step manner for both integer- and fractional-order systems. Theoretical analysis is performed to ensure the method’s convergence and stability. To demonstrate the method’s effectiveness, several illustrative examples are solved. Visual validation is provided through 2D and 3D plots that depict the behavior of the solutions, while numerical error analysis is presented in tabular form. These results reveal that the approximate solutions exhibit strong agreement with the exact ones, with improved accuracy as the number of iterations increases. Detailed discussions of the findings are included to further support the reliability and applicability of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109088"},"PeriodicalIF":3.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501384","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":"Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs","authors":"Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu","doi":"10.1016/j.cnsns.2025.109063","DOIUrl":"https://doi.org/10.1016/j.cnsns.2025.109063","url":null,"abstract":"In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform (MMT) algorithm, analogous to the discrete Fourier transform, which offers a reliable framework for evaluating nonlinearities in spectral methods while effectively mitigating challenges associated with rounding errors. Second, we examine the Zernike polynomials, a spectral basis well-suited for problems on the disk, and highlight their essential properties. We further demonstrate how the MMT approach can be effectively employed to compute the product of truncated Zernike series, ensuring both accuracy and efficiency. Finally, we combine the MMT framework and Zernike series to construct computer-assisted proofs that establish the existence of solutions to two distinct nonlinear elliptic PDEs on the disk.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"27 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503970","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":"AI-driven control of chaos: A transformer-based approach for dynamical systems","authors":"David Valle,&nbsp;Rubén Capeans,&nbsp;Alexandre Wagemakers,&nbsp;Miguel A.F. Sanjuán","doi":"10.1016/j.cnsns.2025.109085","DOIUrl":"10.1016/j.cnsns.2025.109085","url":null,"abstract":"<div><div>Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control bounds required to confine particles within a region indefinitely, using only the first iterations of diverging orbits as required information of the system. This model-free approach achieves high accuracy, with a mean squared error of <span><math><mrow><mn>2</mn><mo>.</mo><mn>88</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math></span> and computation times in the range of seconds. The results highlight its efficiency and potential for real-time control of chaotic systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109085"},"PeriodicalIF":3.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503969","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":"Effect of the internal factors on the spike train correlation of pairwise directly connected neurons in a simplified micro-column model","authors":"Ruyue Wang,&nbsp;Jinling Liang","doi":"10.1016/j.cnsns.2025.109079","DOIUrl":"10.1016/j.cnsns.2025.109079","url":null,"abstract":"<div><div>The spike train correlation of pairwise neurons in the cerebral cortex is tightly related to cognitive abilities. Nowadays, more clarity is needed on the internal influencing mechanism of spike train correlation, especially in pairwise directly connected neurons. To this end, this paper explores effect of the internal factors on the spike train correlation of pairwise directly connected neurons in a micro-column (MC) model. In detail, a simplified MC model with morphology is constructed, then two groups of parameters are set to obtain two specific MCs called MC1 and MC2 respectively, where two output neurons (named as PN4 and PN5 separately) in the MCs are focused on. What is more, a spike count similarity (SCS) metric and a spike time correlation (STC) metric are proposed in this paper to quantify specific spike train correlation patterns with zero time lag. The main simulation results demonstrate that variations of the internal factors (including the synaptic strengths, the synaptic delay, as well as volumes of the soma and axon hillock) affect the spike train correlation to different extents, from which it is inferred that the spike train correlation of directly connected neurons could be effectively modulated by these internal factors. It is further shown that, compared to the inhibitory synapse, existence of the excitatory synapse may be necessary for the appearance of extremely high correlation for spike trains. In a specific range, the SCS metric is a decreasing function concerning the strength of the inhibitory synapse and an increasing function with respect to the strength of the excitatory synapse. In addition, a larger soma volume of PN4 corresponds to a weaker STC. Compared with variations of the volumes concerning the soma and axon hillock, the STC metric is more sensitive to the changes in the synaptic strengths as well as synaptic delays. Unlike the existing ones, the MC model constructed in this paper fully considers the neuronal morphology (such as the dendritic branches) which shapes the intrinsic/dynamical behaviors of the MCs. Furthermore, this established MC model would provide a foundation for investigating the higher-order spike train correlations among multiple neurons. The two metrics proposed here present a novel perspective for analyzing the correlation strength of pairwise spike trains. Also, they can be used to identify certain special spike train correlation patterns that might provide some helpful decoding strategies in the brain computer interface in the future.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109079"},"PeriodicalIF":3.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144503971","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 discrete rogue wave solutions and model parameters of Ablowitz–Ladik equation via symmetric difference data enhancement physics-informed neural networks","authors":"Jian-Chen Zhou,&nbsp;Xiao-Yong Wen,&nbsp;Ping Zhou,&nbsp;Meng-Chu Wei","doi":"10.1016/j.cnsns.2025.109046","DOIUrl":"10.1016/j.cnsns.2025.109046","url":null,"abstract":"<div><div>We introduce an innovative discrete deep learning approach, termed symmetric difference data enhancement physics-informed neural networks (SDE-PINNs), designed to address both forward and inverse problems associated with discrete rogue waves in nonlinear lattice equations. The methodology is characterized by three main contributions: (1) The development of structure-preserving discrete difference operators that maintain intrinsic symmetry within lattice systems, thereby overcoming the limitations of traditional continuous PINNs when applied to discrete environments; (2) To the best of our knowledge, this is the first application of deep learning techniques to inverse problems in discrete systems, achieving coefficient inversion under sparse, low-noise data conditions. Additionally, it was observed that increasing data density enhances robustness against high-noise environments; (3) A comprehensive statistical non-parametric test analysis elucidates the crucial relationship between initialization strategies and model robustness, notably identifying the optimal initialization point as the midpoint between true symmetry and domain boundaries. Through comprehensive numerical experiments and parameter inversion applied to first- and second-order discrete rogue waves within the Ablowitz–Ladik (AL) equation, we demonstrate the method’s ability to attain accuracy levels of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow></math></span> in forward modeling and a parameter recognition rate exceeding 99% in inverse problems. This approach uniquely integrates deep learning with discrete soliton theory, establishing novel connections between the two fields.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109046"},"PeriodicalIF":3.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144490497","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}