Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Bifurcation control for the collective behavior of delayed-coupled agents via PD controller","authors":"Yongjian Zhou,&nbsp;Tao Wang,&nbsp;Xingguang Peng","doi":"10.1016/j.cnsns.2025.108921","DOIUrl":"10.1016/j.cnsns.2025.108921","url":null,"abstract":"<div><div>How to design control algorithms to effectively regulate the collective behavior with sensing delay remains a formidable challenge. In this paper, we propose to use bifurcation control with PD controller to regulate the collective behavior under sensing delay. The controlled system exhibits the emergence of three distinct states. Bifurcation analysis reveals that the Hopf bifurcation and pitchfork bifurcation curves in the parameter space can be effectively manipulated by selecting the appropriate parameters, thereby enabling state transitions within the system. Furthermore, our findings suggest that the PD controller can influence the convergence rate towards the desired system state. Theoretical properties of these three states, in relation to physical parameters, are theoretically derived, and particle simulations are conducted to validate these theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108921"},"PeriodicalIF":3.4,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947836","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 new global optimization algorithm based on space-filling curve and auxiliary function approach and its applications","authors":"Nurullah Yilmaz","doi":"10.1016/j.cnsns.2025.108920","DOIUrl":"10.1016/j.cnsns.2025.108920","url":null,"abstract":"<div><div>Global optimization is a topic of great interest because of the many practical problems in real life. This article focuses on the unconstrained global minimization of multi-modal continuously differentiable functions, an important subclass of global optimization problems. In order to solve these problems, we develop a new global optimization technique that utilizes two fundamental concepts. The first one is the reducing dimension technique, which uses space-filling curves, while the second one involves utilizing an auxiliary function approach. We propose a new continuously differentiable auxiliary function with direct control of the slope and present the theory behind it. The auxiliary function method is combined with the space-filling curve methodology. We construct a new global optimization algorithm based on the proposed auxiliary function, space-filling curves, and local searches. We implement a comprehensive numerical test procedure to evaluate the numerical stabilization and efficiency of the proposed algorithm. For this purpose, the proposed algorithm is applied to test problems, and the obtained numerical results are compared with the results obtained by some recently proposed algorithms. Moreover, the proposed algorithm is applied to two different economic load dispatch problems, and promising results are obtained.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108920"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943242","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":"Standing waves with prescribed mass for NLS equations with Hardy potential in the half-space under Neumann boundary condition","authors":"Yuxuan Zhang ,&nbsp;Xiaojun Chang ,&nbsp;Lin Chen","doi":"10.1016/j.cnsns.2025.108917","DOIUrl":"10.1016/j.cnsns.2025.108917","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Consider the Neumann problem: &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;on&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;with the prescribed mass: &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; denotes the upper half-space in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; is the Hardy potential, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; stands for the outward unit normal vector to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; appears as a Lagrange multiplier. Firstly, by applying Ekeland’s variational principle, we establish the existence of normalized solutions that correspond to local minima of the associated energy functional. Furthermore, we find a second normalized solution of mountain pass type by employing a parameteri","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108917"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947835","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":"Asymptotic behavior of mild solutions to stochastic neutral functional differential equations with delay","authors":"Haide Gou,&nbsp;Min Shi","doi":"10.1016/j.cnsns.2025.108906","DOIUrl":"10.1016/j.cnsns.2025.108906","url":null,"abstract":"<div><div>This paper aims to discuss the existence, uniqueness and continuous dependence of mild solution of a class of non-autonomous stochastic neutral functional differential equations with state-dependent delay. Firstly, by using operator theory and estimates of the nonlinear term, we obtain the existence, uniqueness and continuous dependence of our concern system. Secondly, through the Arzelà–Ascoli theorem, the Schauder fixed point theorem and operator theory, we discuss the global existence asymptotic behavior of mild solution of our concern system. Then, the existence of a global forward attracting set in the mean square topology is discussed. Finally, we give an example to verify the validity of the obtained results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108906"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941878","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":"Finite-time boundedness of fuzzy DP-CPS with input quantization and network attack via fuzzy dynamic parabolic controller approach","authors":"Teng-Fei Li ,&nbsp;Liming Ding ,&nbsp;Xiao-Heng Chang ,&nbsp;Ju H. Park","doi":"10.1016/j.cnsns.2025.108864","DOIUrl":"10.1016/j.cnsns.2025.108864","url":null,"abstract":"<div><div>This paper focuses on the research of nonlinear distributed parameter cyber physical systems (DP-CPS) via finite-time interval. The nonlinearity of the DP-CPS is captured through the utilization of the Takagi–Sugeno (T–S) fuzzy model, which gives rise to a class of fuzzy parabolic partial differential equation (PDE). In order to optimize the network resources, a class of dynamic quantizer is employed to quantize the measurement output and control input signals. Then a fuzzy spatial-dependent dynamic parabolic control strategy with attack is firstly proposed to simplify the control design strategy and address the issue of degraded control performance caused by the inability of traditional control methods to effectively handle spatial variations in system parameters for systems with spatially distributed characteristics. The analysis of finite-time boundedness for the fuzzy parabolic PDE is conducted based on the Lyapunov functional. The finite-time boundedness controller design conditions and the adjustment parameters for the dynamic quantizers are presented for the fuzzy closed-loop system. Additionally, an any given matrix method is employed to decouple the coupled nonlinear terms in the control design conditions. The effectiveness of the proposed control approach has been confirmed through simulation conducted on a cascaded system comprising two cylindrical lithium batteries.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108864"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067227","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":"Privacy preserving prescribed-time consensus in second-order nonlinear multi-agent systems","authors":"Qiang Jia,&nbsp;Shihan Lu,&nbsp;Shuiming Cai","doi":"10.1016/j.cnsns.2025.108918","DOIUrl":"10.1016/j.cnsns.2025.108918","url":null,"abstract":"<div><div>In cooperative systems, information exchange is essential for achieving consensus, and the preservation of data privacy has attracted growing attention. However, most existing studies have been limited to first-order multi-agent systems. This study investigates the privacy-preserving consensus problem of second-order agents with Lipschitz-type nonlinearities. A novel masking scheme based on specific power functions is proposed to conceal the true states of the agents, which differs significantly from existing obfuscation methods. Meanwhile, by integrating a high-gain prescribed-time controller, second-order consensus is achieved within a user-defined time frame. As a consequence, the agents’ initial true states, including positions and velocities, are effectively safeguarded. A sufficient condition is derived for determining the control parameters, thereby elucidating the influence of agent dynamics, network topology, and control parameters. Additionally, despite the presence of high-gain and masking signals, the resulting controllers are proven to be bounded. Finally, several numerical examples are provided to validate the theoretical findings and demonstrate the effectiveness of the proposed control strategies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108918"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067226","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":"Secure impulsive synchronization control of multi-agent systems under switching deception attacks on dual channel","authors":"Jiangyan He ,&nbsp;Xing Guo ,&nbsp;Zili Chen ,&nbsp;Yunbin Kuang","doi":"10.1016/j.cnsns.2025.108922","DOIUrl":"10.1016/j.cnsns.2025.108922","url":null,"abstract":"<div><div>This paper explores the mean-square bounded synchronization problem of leader-following multi-agent systems (LF-MASs) with directed graph under dual-channel stochastic switching deception attacks. Compared to previous studies, a new dual-channel stochastic switching deception attack mode is considered. Under this attack mode, the actuator receives different deception signals sourced from either the sensor-controller (S-C) channel or the controller-actuator (C-A) channel within different impulsive intervals. To tackle this challenging problem, a novel adaptive and switching secure impulsive synchronization control protocol is designed. In this new protocol, the stochastic switching manner obeys the Bernoulli distribution on each channel, and some criteria for the mean-square bounded synchronization of the LF-MASs have been obtained by applying the linear matrix inequality technique, matrix analytic theory and Lyapunov stability theory. Further, under periodically variable impulsive time windows (PVITW), the impact of minor deviations in the triggering moments on the synchronization bounds is discussed. Finally, three examples are given to verify the obtained results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108922"},"PeriodicalIF":3.4,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941880","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":"Novel intelligent exogenous neuro-architecture–driven machine learning approach for nonlinear fractional breast cancer risk system","authors":"Afshan Fida ,&nbsp;Muhammad Asif Zahoor Raja ,&nbsp;Chuan-Yu Chang ,&nbsp;Muhammad Junaid Ali Asif Raja ,&nbsp;Zeshan Aslam Khan ,&nbsp;Muhammad Shoaib","doi":"10.1016/j.cnsns.2025.108955","DOIUrl":"10.1016/j.cnsns.2025.108955","url":null,"abstract":"<div><div>Breast cancer remains one of the most prevalent and life-threatening diseases worldwide, necessitating mathematical modelling frameworks to capture the complexity of its progression and risk factors. This research endeavor uncovers the novel machine learning expedition using an Adaptive Nonlinear AutoRegressive eXogenous (ANARX) neural network on a Fractional Order Breast Cancer Risk (FO-BCR) model. A novel Caputo fractional operator-based breast cancer risk model is presented using a five compartmental system reflected by healthy, tumor, immune, estrogen, and fatty cells. A modified fractional Adams PECE method is opted to generate solutions of the five fractional order variants on the four diverse BCR scenarios. These temporal sequences are parsed as ground truth for the adept ANARX network, which is iteratively refined using the Levenberg-Marquardt (LM) algorithm. The performance evaluation of the temporal feature learning of the ANARX-LM algorithm is comprehensively evaluated against reference numerical outcomes using mean square error (MSE) performance graphics, input-error cross correlation, error autocorrelation, error histogram analysis, sequential response and comparative error analysis charts. Low disparity between reference solutions is observed for all FO-BCR systems, with MSE errors in the range of 10⁻⁸ to 10⁻¹¹. Finally, the ANARX-LM’s predictive prowess is evaluated using the single and multistep configurations. Minute errors in the range of 10⁻⁹ to 10⁻¹¹, 10⁻⁸ to 10⁻¹⁰ suggest accurate anticipation of the FO-BCR system enabling preventive and prognostic measures for breast cancer models. These empirical findings underscore the potential of advanced machine-learning-driven neuro-architecture for next-generation predictive-oncology solutions that may facilitate treatment strategies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108955"},"PeriodicalIF":3.4,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067175","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":"Explicit numerical computation of normal forms for Poincaré maps","authors":"Joan Gimeno ,&nbsp;Àngel Jorba ,&nbsp;Marc Jorba-Cuscó ,&nbsp;Maorong Zou","doi":"10.1016/j.cnsns.2025.108913","DOIUrl":"10.1016/j.cnsns.2025.108913","url":null,"abstract":"<div><div>We present a methodology for computing normal forms in discrete systems, such as those described by Poincaré maps. Our approach begins by calculating high-order derivatives of the flow with respect to initial conditions and parameters, obtained via jet transport, and then applying appropriate projections to the Poincaré section to derive the power expansion of the map. In the second step, we perform coordinate transformations to simplify the local power expansion around a dynamical object, retaining only the resonant terms. The resulting normal form provides a local description of the dynamics around the object, and shows its dependence on parameters. Notably, this method does not assume any specific structure of the system besides sufficient regularity.</div><div>To illustrate its effectiveness, we first examine the well-known Hénon–Heiles system. By fixing an energy level and using a spatial Poincaré section, the system is represented by a 2D Poincaré map. Focusing on an elliptic fixed point of this map, we compute a high-order normal form, which is a twist map obtained explicitly. This means that we have computed the invariant tori inside the energy level of the Poincaré section. Furthermore, we explore how both the fixed point and the normal form depend on the energy level of the Poincaré section, deriving the coefficients of the twist map as a power series of the energy level. This approach also enables us to obtain invariant tori inside nearby energy levels. We also discuss how to obtain the frequencies of the torus for the flow. We include a second example involving an elliptic periodic orbit of the spatial Restricted Three-Body Problem. In this case the map is 4D, and the normal form is a multidimensional twist map.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108913"},"PeriodicalIF":3.4,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936401","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":"Asymptotical behavior of the 2D stochastic partial dissipative Boussinesq system with memory","authors":"Haoran Dai ,&nbsp;Bo You ,&nbsp;Tomás Caraballo","doi":"10.1016/j.cnsns.2025.108916","DOIUrl":"10.1016/j.cnsns.2025.108916","url":null,"abstract":"<div><div>The objective of this paper is to consider the asymptotical behavior of solutions for the two-dimensional partial dissipative Boussinesq system with memory and additive noise. We first establish the existence of a random absorbing set in the phase space. However, due to the presence of the memory term, we cannot obtain some kind of compactness of the corresponding cocycle through Sobolev compactness embedding theorem or by verifying the pullback flattening property. To overcome this difficulty, we first prove the asymptotical compactness of the velocity component of weak solutions, and then we prove the asymptotical compactness of other components based on some energy estimates and the Aubin–Lions compactness lemma, which implies the asymptotical compactness of the corresponding cocycle. Thus, the existence of a random attractor is obtained. Finally, we establish an abstract result about some kind of upper semi-continuity of the random attractor, which is applied to the two-dimensional partial dissipative Boussinesq system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108916"},"PeriodicalIF":3.4,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936253","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}