Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Population dynamics of a logistic model incorporating harvesting pulses on a growing domain","authors":"Han Zhang,&nbsp;Min Zhu","doi":"10.1016/j.cnsns.2025.108768","DOIUrl":"10.1016/j.cnsns.2025.108768","url":null,"abstract":"<div><div>To investigate the impact of the expanding region and harvesting pulses on population dynamics, we propose a one-dimensional logistic model that integrates harvesting pulses on a growing domain. By employing the eigenvalue method, we derive the explicit expression of the ecological reproduction index <span><math><msub><mrow><mi>ℜ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and analyze its pertinent properties. Subsequently, we explore the asymptotic behavior of solutions for both monotonic and nonmonotonic impulsive functions by applying the method of upper and lower solutions, comparison principle, as well as upper and lower systems technique. Our dynamical results reveal that if <span><math><mrow><msub><mrow><mi>ℜ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, the population persists and exhibits periodical behavior; conversely, if <span><math><mrow><msub><mrow><mi>ℜ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the population eventually faces extinction. In numerical simulations, we find that a larger habitat promotes population survival irrespective of the occurrence of pulses, whereas harvesting pulses always restrains population persistence.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108768"},"PeriodicalIF":3.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644005","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":"Unconditionally optimal error estimates of linearized virtual element methods for a class of nonlinear wave equations","authors":"Zhixin Liu ,&nbsp;Minghui Song ,&nbsp;Yuhang Zhang","doi":"10.1016/j.cnsns.2025.108765","DOIUrl":"10.1016/j.cnsns.2025.108765","url":null,"abstract":"<div><div>In this paper, we analyze the unconditionally optimal error estimates of the linearized virtual element schemes for a class of nonlinear wave equations. For the general nonlinear term with non-global Lipschitz continuity, we consider a modified Crank–Nicolson scheme for the time discretization and a conforming virtual element method for the spatial discretization. Using the mathematical induction and the Sobolev embedding inequality, we derive the optimal <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm error estimates without any ratio restrictions between the time step <span><math><mi>τ</mi></math></span> and the space mesh size <span><math><mi>h</mi></math></span>. The key point of our approach is the boundedness of the numerical solution in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm rather than in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm. For the cubic nonlinear term, we develop another linearized scheme using a modified leapfrog scheme in the time direction. We show that this scheme can maintain the energy stability, which directly ensures the boundedness of the numerical solution in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm. And then the unconditionally optimal <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> error estimate is also established. Finally, some numerical examples are given to demonstrate the validity of our methods.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108765"},"PeriodicalIF":3.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642075","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 melting and solidification dynamics in metallic powders during the bed fusion process","authors":"Qing Xia ,&nbsp;Sijing Lai ,&nbsp;Junseok Kim ,&nbsp;Yibao Li","doi":"10.1016/j.cnsns.2025.108762","DOIUrl":"10.1016/j.cnsns.2025.108762","url":null,"abstract":"<div><div>In this study, we introduce a phase field model designed to represent the intricate physical dynamics inherent in selective laser melting processes. Our approach employs a phase-field model to simulate the liquid–solid phase transitions, fluid flow, and thermal conductivity with precision. This model is founded on the variational principle, aiming to minimize the free energy functional, thereby guaranteeing the dissipation of energy. We have developed a complex model that integrates a series of phase field equations, which address the evolution of interfaces and the dynamics of phase transitions. The model also encompasses the Navier–Stokes equations to depict fluid motion and an energy equation to trace the temperature distribution. Critical to the effectiveness of this model is the consideration of the coupling relations among these equations, ensuring a holistic representation of the phenomena. The discretization of the model is achieved through the semi-implicit Crank–Nicolson scheme, which confirms the unconditional energy stability of the system. We have subjected the model to a series of numerical tests, which have validated its capability to accurately capture the evolution of interface morphology, temperature fields, and flow patterns. The results demonstrate numerical stability and efficiency. A central achievement of this research is the establishment of a rigorous proof of unconditional energy stability within the phase-field model tailored for selective laser melting processes. The numerical results affirm the physical accuracy and numerical dependability of the proposed model, which lays a foundation for future simulation endeavors.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108762"},"PeriodicalIF":3.4,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642076","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":"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}