Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Non-confluence for uncertain differential equations","authors":"Zhi Li,&nbsp;Jing Ning,&nbsp;Liping Xu,&nbsp;Linbing Guo","doi":"10.1016/j.cnsns.2025.108760","DOIUrl":"10.1016/j.cnsns.2025.108760","url":null,"abstract":"<div><div>This paper is concerned with a class of non-linear uncertain differential equations driven by canonical process, which is the twin of Brownian motion in the structure of uncertain theory. By the Carathéodory approximation, we prove the existence and uniqueness of solutions for the considered equations under some non-Lipschitz conditions. Subsequently, By applying the chain rule for the considered equation, we introduce and attempt to explore the non-confluence property of the solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions. Finally, two examples are provided to illustrate the effectiveness of our main results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108760"},"PeriodicalIF":3.4,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143643377","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":"Passivity of nabla fractional order systems and its application on distributed optimization","authors":"Haoran Xu,&nbsp;Rui Chen,&nbsp;Xintong Ni,&nbsp;Yiheng Wei","doi":"10.1016/j.cnsns.2025.108747","DOIUrl":"10.1016/j.cnsns.2025.108747","url":null,"abstract":"<div><div>While the passivity of integer-order systems has been extensively analyzed, recent focus has shifted toward exploring the passivity of fractional-order systems. However, a clear definition of Nabla Fractional Order Systems (NFOSs) has not yet been established. In this work, the concepts of passivity, dissipativity, and finite-gain <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>α</mi></mrow></msub></math></span> stability are extended to NFOSs, and relevant theories are proposed. Utilizing nabla fractional calculus and these proposed theories, a passivity-based approach is developed to study distributed optimization in nonlinear multi-agent systems experiencing observational disturbances.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108747"},"PeriodicalIF":3.4,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642078","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":"Strong order one convergence of the projected Euler–Maruyama method for the Wright–Fisher model","authors":"Yiyi Tang","doi":"10.1016/j.cnsns.2025.108759","DOIUrl":"10.1016/j.cnsns.2025.108759","url":null,"abstract":"<div><div>The Wright–Fisher model is a useful SDE model, and it has many applications in finance and biology. However, it does not have an analytical solution currently. In this paper, we introduce a boundary preserving numerical method, called the projected EM method, to simulate it. We first use the projected EM method for the Lamperti transformed Wright–Fisher model. Then generated numerical solutions are transformed to derive the numerical approximations for the original Wright–Fisher model. We will use a new numerical analysis method to prove uniformly bounded inverse moments of the projected EM numerical solution, and then study the strong convergence of the projected EM method. Compared to existing explicit EM methods for the Wright–Fisher model, the projected EM method is strongly convergent with order one in more general <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm and for more parameter settings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108759"},"PeriodicalIF":3.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636516","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 evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers–Moyal formulas","authors":"Yang Li ,&nbsp;Shengyuan Xu ,&nbsp;Jinqiao Duan","doi":"10.1016/j.cnsns.2025.108751","DOIUrl":"10.1016/j.cnsns.2025.108751","url":null,"abstract":"<div><div>Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise from data is challenging due to the possible intricate functional forms and the inherent complexity of Lévy motion. This research endeavors to develop an evolutionary symbolic sparse regression (ESSR) approach to extract non-Gaussian stochastic dynamical systems from sample path data, based on nonlocal Kramers–Moyal formulas, genetic programming, and sparse regression. Specifically, genetic programming is employed to generate a diverse array of candidate functions, sparse regression is used to learn the coefficients associated with these candidates, and the nonlocal Kramers–Moyal formulas serve as the foundation for constructing the fitness measure in genetic programming and the loss function in sparse regression. The efficacy and capabilities of this approach are demonstrated through its application to several illustrative models. This approach stands out as a powerful tool for deciphering non-Gaussian stochastic dynamics from available datasets, suggesting a wide range of applications across various fields.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108751"},"PeriodicalIF":3.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620546","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":"Nonconforming finite element method for a 4th-order history-dependent hemivariational inequality","authors":"Jiali Qiu ,&nbsp;Min Ling ,&nbsp;Fei Wang ,&nbsp;Bangmin Wu","doi":"10.1016/j.cnsns.2025.108750","DOIUrl":"10.1016/j.cnsns.2025.108750","url":null,"abstract":"<div><div>This paper explores the analysis and numerical solution of a fourth-order history-dependent hemivariational inequality. The variational formulation is derived from a model describing an elastic plate in contact with a reactive obstacle, where the contact condition involves both the subdifferential of a nonconvex, nonsmooth function and a Volterra-type integral term. We discretize the continuous formulation using the left rectangle rule to handle the history-dependent operator, along with a Morley finite element method for spatial discretization. A priori error estimates for the fully discrete scheme are established, demonstrating optimal convergence. Numerical examples are provided to verify the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108750"},"PeriodicalIF":3.4,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618170","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":"Wave of chaos and Turing patterns in Rabbit–Lynx dynamics: Impact of fear and its carryover effects","authors":"Ranjit Kumar Upadhyay,&nbsp;Namrata Mani Tripathi,&nbsp;Dipesh Barman","doi":"10.1016/j.cnsns.2025.108748","DOIUrl":"10.1016/j.cnsns.2025.108748","url":null,"abstract":"<div><div>An attempt has been made to understand the joint impact of predator induced fear and its carryover consequences with diffusion. The prey population such as European rabbit is captured and consumed by the predator, Iberian lynx. In the absence of diffusion, the system undergoes saddle–node and Hopf-bifurcation with respect to the carryover and fear parameters. Both the fear and carryover parameter affect the system dynamics in a contradictory manner, i.e., higher amount of fear level destabilizes the system dynamics whereas higher amount of carryover level stabilizes it. Additionally, the creation and destruction of interior equilibrium points have been observed under the variation of both these parameters independently. Furthermore, the temporal system undergoes Cusp bifurcation in two parametric plane such as <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mi>δ</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mi>δ</mi></mrow></math></span> plane. The global stability of the temporal system has been analyzed both analytically and numerically. However, in the presence of diffusion, the system experiences Turing instability. Numerical simulation shows the occurrence of spatio-temporal pattern formation for the proposed system. Further, it exhibits wave of chaos phenomenon for lower level of fear and carryover parameter value which is very important phenomenon to understand the spread of disease dynamics. Furthermore, the effect of the predator induced fear on the system dynamics has been explored in non-local sense for the spatio-temporal system. Our research integrates the model dynamics with its analysis by a variety of figures and diagrams that visually represent and reinforce our results. By examining non-linear models, we reveal unique and noteworthy patterns that offer fresh perspectives. These discoveries are particularly useful for biologists aiming to deepen their understanding of eco-epidemiological system dynamics in a practical context. The graphical depictions throughout our study play a key role in delivering a thorough analysis, making the findings more approachable and relevant to both researchers and field practitioners.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108748"},"PeriodicalIF":3.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609769","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":"Modeling and simulation of the conserved N-component Allen–Cahn model on evolving surfaces","authors":"Lulu Liu,&nbsp;Xufeng Xiao,&nbsp;Xinlong Feng","doi":"10.1016/j.cnsns.2025.108745","DOIUrl":"10.1016/j.cnsns.2025.108745","url":null,"abstract":"<div><div>This paper establishes the conserved N-component Allen–Cahn model on evolving surfaces and conducts numerical simulations of the model. In mathematical modeling, since the surface motion velocity causes local contraction or expansion of the surface, it is hard to simultaneously fulfill the componential mass conservation and the point-wise mass conservation as the usual case on the static domain. Therefore, according to these two types of conservation, three models are established: the componential mass conservation model, the point-wise mass conservation model, and the componential and point-wise mass conservation model. For the numerical simulation, the evolving surface finite element method is used to discretize the model in time and space. To achieve a stable, linear, high-accuracy and decoupled numerical scheme, the evolving surface finite element method has been enhanced by incorporating the stabilized semi-implicit approach. Furthermore, the stability analysis has been undertaken to validate the robustness of the devised numerical scheme. Through the validation of numerous numerical simulations, the reasonableness of the proposed model and the efficacy of the numerical approach are evaluated.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108745"},"PeriodicalIF":3.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618159","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":"Synchronization in predefined time of octonion-valued competitive neural networks: Aperiodic complete intermittent control and non-separation method","authors":"Hongyun Yan ,&nbsp;Yuanhua Qiao ,&nbsp;Lan Wang ,&nbsp;Qiang Li","doi":"10.1016/j.cnsns.2025.108746","DOIUrl":"10.1016/j.cnsns.2025.108746","url":null,"abstract":"<div><div>In this paper, a class of competitive neural network models based on octonions is first constructed, and its predefined-time synchronization is explored by applying non-separation method and aperiodic complete intermittent control. Based on classification analysis and measurable selection theory, two novel equalities regarding octonion algebra are developed, which play a key role in studying the synchronization of octonion-valued systems using non-separation method and controllers with sign functions. Additionally, a new predefined-time stability lemma is proposed for systems with aperiodic complete intermittent controllers by utilizing mathematical induction. Then, two type of octonion-valued aperiodic complete intermittent controllers are designed for the first time to induce the predefined-time synchronization of the constructed model. Meanwhile, some new criteria for predefined-time synchronization are deduced. Finally, the effectiveness of the theoretical results is verified by a numerical example.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108746"},"PeriodicalIF":3.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609768","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":"Strang splitting structure-preserving high-order compact difference schemes for nonlinear convection diffusion equations","authors":"Baolin Kuang ,&nbsp;Shusen Xie ,&nbsp;Hongfei Fu","doi":"10.1016/j.cnsns.2025.108749","DOIUrl":"10.1016/j.cnsns.2025.108749","url":null,"abstract":"<div><div>In this paper, by using the Lagrange multiplier approach and the operator splitting method, we construct some structure-preserving high-order and efficient compact difference schemes for nonlinear convection diffusion equations. For the one-dimensional model problem, we first introduce a high-order compact Strang splitting scheme (denoted as HOC-Splitting), which is fourth-order accurate in space and second-order accurate in time. Then, by incorporating the Lagrange multiplier approach with the HOC-Splitting scheme, we construct two additional bound-preserving or/and mass-conservative HOC-Splitting schemes that do not require excessive computational cost and can automatically ensure the uniform bounds of the numerical solution. These schemes combined with an alternating direction implicit (ADI) method are generalized to the two-dimensional model problem, further enhancing the computational efficiency for large-scale modeling and simulation. Finally, ample numerical examples are presented to verify the accuracy, efficiency, and effectiveness in preserving bounds or/and mass of the proposed schemes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108749"},"PeriodicalIF":3.4,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642077","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 fully discrete finite element method for unsteady magnetohydrodynamic flow in porous media","authors":"Qianqian Ding ,&nbsp;Shipeng Mao ,&nbsp;Xiaorong Wang","doi":"10.1016/j.cnsns.2025.108735","DOIUrl":"10.1016/j.cnsns.2025.108735","url":null,"abstract":"<div><div>This article explores the unsteady magnetohydrodynamic (MHD) model within the framework of porous media flow. This model consists of the Brinkman–Forchheimer equations and Maxwell equations in the porous media domain, which are coupled by the Lorentz force. We propose and analyze a numerical discretization method for MHD porous model. The second-order backward difference formula is utilized for temporal derivative terms, and the mixed finite element method is employed for spatial discretization. Rigorous proofs of stability and uniqueness are provided for the numerical solutions. We establish optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error estimates for the velocity and magnetic induction without imposing constraints on the relationship between the time step and mesh size. Finally, several three-dimensional numerical experiments are performed to illustrate the features of the proposed numerical method and validate the theoretical findings. To our knowledge, this is the first error analysis and simulation to address unsteady MHD flow through porous media.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108735"},"PeriodicalIF":3.4,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577254","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}