Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Superconvergence analysis and extrapolation of a BDF2 fully discrete scheme for nonlinear reaction–diffusion equations","authors":"Conggang Liang ,&nbsp;Dongyang Shi","doi":"10.1016/j.cnsns.2024.108446","DOIUrl":"10.1016/j.cnsns.2024.108446","url":null,"abstract":"<div><div>The main aim of this paper is to propose a 2-step backward differential formula (BDF2) fully discrete scheme with the bilinear <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>11</mn></mrow></msub></math></span> finite element method (FEM) for the nonlinear reaction–diffusion equation. By use of the combination technique of the element’s interpolation and Ritz projection, and through the interpolation post-processing approach, the superclose and global superconvergence estimates with 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> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm are deduced rigorously. Furthermore, with the help of the asymptotic error expansion of the <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>11</mn></mrow></msub></math></span> element, a new suitable fully discrete scheme is developed, and the extrapolation result of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm is derived, which is one order higher than that of the above traditional superconvergence estimate with respect to <span><math><mi>h</mi></math></span>. Here <span><math><mi>h</mi></math></span> is the mesh size and <span><math><mi>τ</mi></math></span> is the time step. Finally, some numerical results are provided to verify the theoretical analysis. It seems that the extrapolation of the fully discrete finite element scheme has never been seen in the previous studies.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108446"},"PeriodicalIF":3.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679156","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":"Global dynamics of a generalized arbitrary order Van der Pol–Duffing Oscillator","authors":"Jueliang Zhou ,&nbsp;Lan Zou","doi":"10.1016/j.cnsns.2024.108445","DOIUrl":"10.1016/j.cnsns.2024.108445","url":null,"abstract":"<div><div>We study the global bifurcation diagram and corresponding global phase portraits in the Poincaré disc for a generalized van der Pol-Duffing oscillator, which has four nonlinear terms with arbitrary orders. This nonlinear oscillator possesses more diverse and complicated dynamical behaviours, including the heteroclinic bifurcation, generalized Hopf bifurcation and pitchfork bifurcation. Moreover, theoretical results are exhibited via numerical simulations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108445"},"PeriodicalIF":3.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679157","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":"Effective 1D-equation with a Lambert W function nonlinearity for cigar-shaped Bose–Einstein condensates","authors":"Hugo L.C. Couto ,&nbsp;Ardiley T. Avelar ,&nbsp;Wesley B. Cardoso","doi":"10.1016/j.cnsns.2024.108447","DOIUrl":"10.1016/j.cnsns.2024.108447","url":null,"abstract":"<div><div>In this paper, we derive an effective 1D equation based on the work of Mateo and Delgado [Phys. Rev. A 77, 013617 (2008)] that governs the axial dynamics of mean-field cigar-shaped Bose–Einstein condensates (BECs) with repulsive interatomic interactions and subject to transverse anti-Gaussian confining potential. The resulting equation exhibits a nonstandard nonlinearity written in terms of the principal branch of the Lambert W function. This equation appropriately encompasses the correct limits within the Thomas–Fermi (TF) and perturbative regimes. The validity of our findings was established through a comparative analysis with numerical solutions derived from the complete three-dimensional Gross–Pitaevskii equation, including those about the limiting cases encountered in the TF and perturbative regimes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108447"},"PeriodicalIF":3.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679159","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":"Robust fault-tolerant control for switched systems based on adaptive unknown input observer","authors":"Yujun Zhao ,&nbsp;Guochen Pang ,&nbsp;Xiangyong Chen ,&nbsp;Jianlong Qiu ,&nbsp;Jinde Cao","doi":"10.1016/j.cnsns.2024.108416","DOIUrl":"10.1016/j.cnsns.2024.108416","url":null,"abstract":"<div><div>This paper investigates the problem of fault diagnosis and fault-tolerant control in switched systems with actuator fault under unknown input disturbances. Initially, an adaptive unknown input observer capable of rapidly estimating faults was designed, incorporating proportional terms to enhance the response speed of fault estimation. Subsequently, by employing the average dwell time approach and using Lyapunov functions, the globally uniformly asymptotically stable of the error system under the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance index was proven. Following this, a state feedback controller was constructed using the state and error estimates from the observer, thereby guaranteeing closed-loop system stability even when faults occur. Finally, the effectiveness of the proposed method was validated through simulation examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108416"},"PeriodicalIF":3.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679162","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":"Fractional pseudo-parabolic equation with memory term and logarithmic nonlinearity: Well-posedness, blow up and asymptotic stability","authors":"Huafei Di ,&nbsp;Yi Qiu ,&nbsp;Liang Li","doi":"10.1016/j.cnsns.2024.108450","DOIUrl":"10.1016/j.cnsns.2024.108450","url":null,"abstract":"<div><div>Considered herein is the initial–boundary value problem for a fractional pseudo-parabolic equation with memory term and logarithmic nonlinearity given by <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>t</mi><mo>−</mo><mi>τ</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mrow><mo>(</mo><mi>τ</mi><mo>)</mo></mrow><mspace></mspace><mi>d</mi><mi>τ</mi><mo>+</mo><mi>u</mi><mo>ln</mo><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow></math></span> under different initial energy levels. The local well-posedness of weak solution is firstly established by using Galerkin approximation and contraction mapping principle at arbitrary initial energy level. Secondly, the global well-posedness, polynomial and exponential energy decay estimates, finite time blow up are investigated at low initial energy level (<span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>δ</mi><mo>,</mo><mn>1</mn></mrow></msub></mrow></math></span>) by utilizing modified potential well theory, Galerkin approximation, perturbed energy method, differential–integral inequality technique etc. Subsequently, based on the above conclusions of low initial energy, the global existence, polynomial and exponential energy decay estimates and finite time blow up are also derived at critical initial energy level (<span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>δ</mi><mo>,</mo><mn>2</mn></mrow></msub></mrow></math></span>) by introducing some new approximation methods and techniques. Here, the sets <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>δ</mi><mo>,</mo><mi>i</mi></mrow></msub></math></span> <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span> defined in Section <span><span>2.2</span></span> denote potential well families involving the parameter <span><math><mrow><mi>δ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. Finally, we give a series of numerical examples used to illuminate above theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108450"},"PeriodicalIF":3.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679158","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":"Security-based control design for synchronization of switched reaction diffusion neural networks with hybrid attacks","authors":"V.T. Elayabharath ,&nbsp;T. Satheesh ,&nbsp;P. Sozhaeswari ,&nbsp;R. Sakthivel ,&nbsp;Y. Ren","doi":"10.1016/j.cnsns.2024.108441","DOIUrl":"10.1016/j.cnsns.2024.108441","url":null,"abstract":"<div><div>This study delves into exploring dissipative synchronization for a class of switched neural networks with external disturbances featuring reaction–diffusion terms under the master–slave scheme. Precisely, the addressed network model comprises a hybrid attack model which entails both deception and denial-of-service attacks. Moreover, security-based control is designed to achieve the intended results, wherein in the realm of control design, the likelihood of cyber attacks is dictated by two separate and independent stochastic Bernoulli distributed factors. Meanwhile, the dissipative theory is employed to effectively curb the external disturbances within the network model. Subsequently, by leveraging the Lyapunov stability theory and linear matrix inequality approach, adequate conditions are acquired for ensuring the mean square exponential synchronization and strict <span><math><mrow><mo>(</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></mrow></math></span>-<span><math><mi>θ</mi></math></span> dissipativity of the examined system. Furthermore, the relation for deriving the control gain matrices is set forth in accordance with the acquired criteria. At the end, a numerical example accompanied by simulation results is supplied to vividly demonstrate the efficacy and significance of the acquired theoretical insights.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108441"},"PeriodicalIF":3.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of network topology in consumer-resource systems with species’ dispersal and evolution","authors":"Weiting Song ,&nbsp;Shikun Wang ,&nbsp;Yuanshi Wang","doi":"10.1016/j.cnsns.2024.108444","DOIUrl":"10.1016/j.cnsns.2024.108444","url":null,"abstract":"<div><div>This paper considers consumer-resource systems, where the consumer moves on a fully-connected patch network and behaves like an agent. Using graph-theoretical method and dynamical systems theory, we show global equilibrium stability in the system. Analysis on the equilibrium demonstrates that when the dispersal rate is small, the effect of network topology is the result of the effect of each path in isolation. It is shown that varying network topology could lead to persistence and/or increase of the consumer. Moreover, agent-based selection on a network would make the network evolve to an evolutionary stable topology, where any small deviation to it will not lead to the increase of species. Our results have potential application in constructing ecological corridors and planning network topology under evolution.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108444"},"PeriodicalIF":3.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652262","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":"Superconvergence analysis of low order nonconforming finite element method for coupled nonlinear semiconductor device problem","authors":"Xiangyu Shi ,&nbsp;Peng Jian ,&nbsp;Dongyang Shi","doi":"10.1016/j.cnsns.2024.108448","DOIUrl":"10.1016/j.cnsns.2024.108448","url":null,"abstract":"<div><div>A linearized decoupled fully discrete scheme is developed and investigated for the coupled nonlinear semiconductor device problem with low order nonconforming <span><math><mrow><mi>E</mi><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>r</mi><mi>o</mi><mi>t</mi></mrow></msubsup></mrow></math></span> element. Then, by use of its special property: the consistency error in the broken <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm can reach to second order when the exact solutions belong to <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, just one order higher than its interpolation error, together with some proper approaches such as the discrete derivative transfer trick, difference quotient between two adjacent time levels, mathematics induction method and so on, the difficulty caused by the nonlinearity is ingeniously coped with, and the superclose estimates about the related variables are derived rigorously. In addition, the satisfactory global superconvergence results are obtained through the interpolation postprocessing approach. Finally, a numerical example is presented to validate the theoretical analysis and the good performance of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108448"},"PeriodicalIF":3.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679160","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 multi-objective optimization approach for multi-zone control of sound fields with uniformity constraint","authors":"Zexi Tang ,&nbsp;Fusheng Bai ,&nbsp;Xiangning Liao ,&nbsp;Hao Luo ,&nbsp;Quanyu Bai","doi":"10.1016/j.cnsns.2024.108443","DOIUrl":"10.1016/j.cnsns.2024.108443","url":null,"abstract":"<div><div>Personal audio systems have been studied extensively since their inception nearly three decades ago. Acoustic Contrast Control (ACC) method is extensively employed due to its capability to establish a distinct contrast in acoustic energy between bright and dark zones. But it fails to ensure a uniform sound field distribution within the bright zone, potentially compromising the auditory comfort experienced by users. To address this issue, some methods have proposed to integrated a bright zone consistency constraint into the ACC model. However, the same parameter across all frequency points are employed in these methods, resulting in the failure to find the optimal solution at many frequency points. In this study, a multi-objective optimization approach is introduced to find the optimal solution at each frequency point. A set of Pareto optimal solutions at each frequency point can be generated by the multi-objective optimization method. This set reflects the trade-off between the two objectives, and allows the decision maker to select the most appropriate solution for real applications based on the importance of the objectives. The goal programming method is adopted to do the selection. Simulation results within a car cabin demonstrate that the proposed method can balance the acoustic contrast and uniformity effectively.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108443"},"PeriodicalIF":3.4,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699676","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":"Dynamics and synchronization of the Morris-Lecar model with field coupling subject to electromagnetic excitation","authors":"Lixiang Wei ,&nbsp;Dong Li ,&nbsp;Jiangang Zhang","doi":"10.1016/j.cnsns.2024.108457","DOIUrl":"10.1016/j.cnsns.2024.108457","url":null,"abstract":"<div><div>In this study, we extend the Morris-Lecar (M-L) neuron model to design a neuronal network model with field effects. Using Lyapunov theory and the master stability function to evaluate the stability of synchronous manifolds. The Hamilton energy function of a single neuron is derived using Helmholtz's theorem to equivalently describe its internal field energy, and bioelectric activities are analyzed in conjunction with synchronization error functions. A comprehensive analysis was conducted using various numerical methods, including time series diagrams, bifurcation diagrams, two-parameter plane synchronization error diagrams, and similarity function diagrams. The observations indicate that variations in conductivity and equilibrium potential directly impact the firing patterns and synchronization states of neurons. In various coupling methods, an increase in coupling strength induces different degrees of oscillation within the coupled system. The effects of three coupling methods on the synchronization of the neuronal network are examined using spatiotemporal evolution diagrams and energy evolution diagrams. Global synchronization error and synchronization factors are introduced to quantify the level of synchrony. Numerical results indicate that an appropriate coupling strength and ionic conductance enhance network synchrony. Numerical results indicate that appropriate coupling strength promotes network synchrony. The insights gained from this study contribute to providing a more coherent framework for constructing neuronal network models under field-coupled conditions, thereby enhancing the understanding of fundamental principles in neuroscience and offering new perspectives for the treatment and rehabilitation of neurological disorders.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"140 ","pages":"Article 108457"},"PeriodicalIF":3.4,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652261","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}