Communications in Nonlinear Science and Numerical Simulation最新文献

{"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}

{"title":"∂̄-dressing method for the coupled third-order flow equation of the Kaup–Newell system","authors":"Jin-Jin Mao","doi":"10.1016/j.cnsns.2025.108841","DOIUrl":"10.1016/j.cnsns.2025.108841","url":null,"abstract":"<div><div>In this article, we investigate the nonlinear spectral properties of the coupled third-order flow of the Kaup–Newell (TOFKN) system by formulating a local matrix <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-equation with non-normalized boundary conditions and two linear constraint equations. Furthermore, we derive a coupled Kaup–Newell hierarchy with sources using recursive operator. By employing a specially designed spectral transformation matrix and the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method, we construct the <span><math><mi>N</mi></math></span>-soliton solutions of the coupled TOFKN system, providing explicit expressions for the one- and two-soliton solutions. These findings demonstrate the effectiveness of the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-dressing method in capturing the complex nonlinear dynamics of the TOFKN system, offering new insights into its soliton interactions and stability properties.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108841"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943244","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":"Refining extinction criteria in a complex multi-stage epidemic system with non-Gaussian Lévy noise","authors":"Yassine Sabbar","doi":"10.1016/j.cnsns.2025.108911","DOIUrl":"10.1016/j.cnsns.2025.108911","url":null,"abstract":"<div><div>This paper proposes a new approach for analyzing extinction conditions in multi-stage epidemic models, incorporating stochastic noises to account for sudden environmental or population-level changes that influence infection transmission. By utilizing an <span><math><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional perturbed system that captures both gradual amelioration and proportional jumps, the research establishes sharp extinction criteria, refining the assumptions typically found in existing literature. Moving away from classical methods that rely on ergodicity, this framework employs moment analysis of the average solution time for an auxiliary equation, effectively addressing the challenges arising from the lack of an explicit expression of the invariant measure. The theoretical results are compared with those from previous studies, and numerical simulations, particularly focused on AIDS/HIV, serve to confirm and reinforce the findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108911"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941879","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":"Error analysis of a fractional-step method for reactive fluid flows with Arrhenius activation energy","authors":"Mofdi El-Amrani ,&nbsp;Anouar Obbadi ,&nbsp;Mohammed Seaid ,&nbsp;Driss Yakoubi","doi":"10.1016/j.cnsns.2025.108867","DOIUrl":"10.1016/j.cnsns.2025.108867","url":null,"abstract":"<div><div>Propagation problems of reaction fronts in viscous fluids are crucial in many industrial and chemical engineering processes. The interactions between the reaction properties and the fluid dynamics yield a complex and nonlinear model of Navier–Stokes equations for the flow with a strong coupling with two reaction–advection–diffusion equations for the temperature and the degree of conversion. To alleviate difficulties related to the numerical approximation of such systems, we propose a fractional-step method to split the problem into several substeps, and based on a viscosity-splitting approach that separates the convective terms from the diffusion terms during the time integration. A first-order scheme is employed for the time integration of each substep of the proposed fractional-step method. The proposed method also preserves the full original boundary conditions for the velocity which eliminates any potential inconsistencies on the pressure, and it allows for nonhomogeneous Dirichlet and Neumann boundary conditions for the temperature and degree of conversion that are physically more appealing. In the present work, we perform an error analysis and provide error estimates for all involved solutions in their relevant norms. A rigorous stability analysis is also carried out in this study and the proposed method is demonstrated to be consistent and stable with no restrictions on the time step. Numerical results obtained for a problem with known analytical solutions are presented to verify the theoretical analysis and to assess the performance of the proposed method. The method is also implemented for solving a two-dimensional flame-like propagation problem in viscous fluids. The obtained computational results for both examples support the theoretical expectations for a stable and accurate numerical solver for reactive fluids with Arrhenius activation energy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108867"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936252","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 innovative low-order H1-Galerkin mixed finite element framework for superconvergence analysis in nonlinear Klein–Gordon equations","authors":"Yanmi Wu,&nbsp;Xin Ge","doi":"10.1016/j.cnsns.2025.108912","DOIUrl":"10.1016/j.cnsns.2025.108912","url":null,"abstract":"<div><div>A <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Galerkin mixed finite element method (MFEM) is explored for solving the nonlinear Klein–Gordon equation, utilizing the lower-order bilinear element paired with the zero-order Raviart–Thomas element <span><math><mrow><mo>(</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>11</mn></mrow></msub><mo>+</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>10</mn></mrow></msub><mspace></mspace><mo>×</mo><mspace></mspace><msub><mrow><mi>Q</mi></mrow><mrow><mn>01</mn></mrow></msub><mo>)</mo></mrow></math></span>. The existence and uniqueness of the solutions for the discretized system are rigorously established. By exploiting the integral identity associated with the bilinear element, a superconvergence estimate linking the interpolation and the Riesz projection is derived. In the semi-discrete framework, the supercloseness of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> is achieved for the primary variable <span><math><mi>u</mi></math></span> in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm and for the auxiliary variable <span><math><mrow><mover><mrow><mi>p</mi></mrow><mo>→</mo></mover><mo>=</mo><mo>∇</mo><mi>u</mi></mrow></math></span> in the <span><math><mrow><mi>H</mi><mrow><mo>(</mo><mtext>div</mtext><mo>;</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> norm, respectively. Additionally, global superconvergence results are obtained through an interpolation-based postprocessing method. Moving to the fully discrete formulation, a second-order scheme is introduced, which exhibits the supercloseness of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>h</mi></math></span> represents the subdivision parameter and <span><math><mi>τ</mi></math></span> the time increment. Finally, the numerical experiments are conducted to confirm the validity of the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108912"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936250","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":"Using Lagrangian descriptors to reveal the phase space structure of dynamical systems described by fractional differential equations: Application to the Duffing oscillator","authors":"Dylan Theron ,&nbsp;Hadi Susanto ,&nbsp;Makrina Agaoglou ,&nbsp;Charalampos Skokos","doi":"10.1016/j.cnsns.2025.108848","DOIUrl":"10.1016/j.cnsns.2025.108848","url":null,"abstract":"<div><div>We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian descriptors method to study the phase space structure of the unforced and undamped Duffing oscillator when fractional-order differential equations govern its time evolution. Our study considers the Riemann–Liouville and the Caputo fractional derivatives. We use the Grünwald–Letnikov derivative, which is an operator represented by an infinite series, truncated suitably to a finite sum as a finite difference approximation of the Riemann–Liouville operator, along with a correction term that approximates the Caputo fractional derivative. While there is no issue with forward-time integrations needed for the evaluation of Lagrangian descriptors, we discuss in detail ways to perform the non-trivial task of backward-time integrations and implement two methods for this purpose: a ‘nonlocal implicit inverse’ technique and a ‘time-reverse inverse’ approach. We analyze the differences in the Lagrangian descriptors results due to the two backward-time integration approaches, discuss the physical significance of these differences, and eventually argue that the ‘nonlocal implicit inverse’ implementation of the Grünwald–Letnikov fractional derivative manages to reveal the phase space structure of fractional-order dynamical systems correctly.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108848"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144067177","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":"Disturbance observer-based H∞ quantized fuzzy control of nonlinear delayed parabolic PDE systems","authors":"Xiaoyu Sun ,&nbsp;Chuan Zhang ,&nbsp;Huaining Wu ,&nbsp;Xianfu Zhang","doi":"10.1016/j.cnsns.2025.108909","DOIUrl":"10.1016/j.cnsns.2025.108909","url":null,"abstract":"<div><div>This research presents a novel quantized fuzzy control technique based on Luenberger-like disturbance observer for a class of nonlinear delayed parabolic partial differential equation (PDE) systems, which are influenced by two distinct types of disturbances. To begin with, the PDE system is decomposed using the Galerkin approach, resulting in a finite-dimensional slow ordinary differential equation (ODE) subsystem and an infinite-dimensional fast ODE subsystem. Then, the slow system which effectively characterizes the active mechanical behavior of the initial model is fuzzified by the Takagi–Sugeno fuzzy technique to obtain a relatively accurate model. Subsequently, based on disturbance observer, three types of quantized fuzzy controllers are devised to ensure that the system become semi-globally uniformly ultimately bounded. Furthermore, the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance control problem with different quantizers is investigated in this study. Lastly, the numerical simulation demonstrates the effectiveness of the three quantizers.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108909"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929618","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":"Resilient discontinuous event-triggering control for exponential stabilization of memristive neural networks under denial-of-service attacks","authors":"Yanyan Ni,&nbsp;Zhen Wang","doi":"10.1016/j.cnsns.2025.108903","DOIUrl":"10.1016/j.cnsns.2025.108903","url":null,"abstract":"<div><div>This paper studies the exponential stabilization issue of memristive neural networks (MNNs) in the presence of denial-of-service (DoS) attacks by using an event-triggering scheme. Unlike the existing event-triggering strategies, not only does the devised resilient discontinuous event-triggering (RDET) scheme avoid the Zeno phenomenon and reduce network communication resource utilization, but can it effectively deal with the non-periodic DoS attacks. In the joint framework of RDET control and DoS attacks, a closed-loop MNNs system is established. Then, to address the attacks in different scenarios, two different-interval-dependent functionals are established. The continuity of functionals improves the anti-attack rate compared with the previous work. Moreover, by using a combination of the convex combination and the estimation techniques, the exponential stabilization results are deduced and a secure controller associated with event-triggering parameters are co-designed. Finally, simulations are carried out to demonstrate the effectiveness of the derived stabilization results and the practical advantages of the proposed RDET scheme subject to DoS attacks.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108903"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929617","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}