Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface","authors":"","doi":"10.1016/j.cnsns.2024.108283","DOIUrl":"10.1016/j.cnsns.2024.108283","url":null,"abstract":"<div><p>In this paper, we present a comprehensive study of the fingering phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface. A theoretical analysis is firstly carried out and the governing equation describing the film thickness is established for the non-Newtonian fluid denoted by a power-law index <span><math><mi>n</mi></math></span>. Using the lubrication theory with dimensionless variables, the partial differential equation for the film thickness is derived, and both two-dimensional flow and three-dimensional flow are investigated. The traveling wave characteristic of the two-dimensional flow is displayed by using the finite difference scheme associated with a Newton iteration technique. The effect of changing the radius of the cylinder, precursor-layer thickness and power-law index is then considered through examining the variation of the capillary waves. Furthermore in three-dimensional complex flow, the fingering patterns for different parameters are simulated. The linear stability analysis based on the traveling wave solutions is given to elucidate the influence of different physical parameters, explaining the physical mechanism of nonlinear flow behaviors in two dimension and three dimension. Results from linear stability analysis show that the power-law index reinforces the fingering instability whether the fluid is shear-thinning or shear-thickening. Moreover, the numerical results illustrate that increasing the radii of the cylinder expands the unstable region. The flow profiles for different power-law coefficients are consistent with the result of the linear stability analysis, proving the unstable role of the power-law coefficient.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020701","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":"Pulse vaccination in a SIR model: Global dynamics, bifurcations and seasonality","authors":"","doi":"10.1016/j.cnsns.2024.108272","DOIUrl":"10.1016/j.cnsns.2024.108272","url":null,"abstract":"<div><p>We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion <span><math><mi>p</mi></math></span> of vaccinated individuals and the time <span><math><mi>T</mi></math></span> between doses. If the <em>basic reproduction number</em> is less than 1 (<em>i.e</em> <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span>), then we obtain precise conditions for the existence and global stability of a disease-free <span><math><mi>T</mi></math></span><em>-periodic</em> solution. Otherwise, if <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, then a globally stable <span><math><mi>T</mi></math></span><em>-periodic</em> solution emerges with positive coordinates.</p><p>We draw a bifurcation diagram <span><math><mrow><mo>(</mo><mi>T</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></math></span> and we describe the associated bifurcations. We also find analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. In a realistic context, low vaccination coverage and intense seasonality may result in unpredictable dynamics. Previous experiments have suggested chaos in periodically-forced biological impulsive models, but no analytic proof has been given.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S100757042400457X/pdfft?md5=25b6d7ba2d7aa1a3e9de0a8c3d41474b&pid=1-s2.0-S100757042400457X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142039799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A bilinear modeling in counts time series with applications","authors":"","doi":"10.1016/j.cnsns.2024.108282","DOIUrl":"10.1016/j.cnsns.2024.108282","url":null,"abstract":"<div><p>This paper introduces a modified bilinear model for integer-valued time series in which thinning operators are applied in bilinear terms involving the product of the input and state process separately. The proposed model is able to consider overdispersion. Furthermore, it connects a feature of the integer-valued autoregressive conditional heteroskedasticity and integer-valued autoregressive processes. Important properties of the proposed model as well as the sufficient condition for stationarity are derived. After considering some estimation methods based on time domain and frequency domain approaches, simulation studies are conducted to check the performance of the estimates. The analysis of practical cases in social science is accomplished to highlight the usefulness of the proposed model in applications, and the model’s adequacy is provided. Further, the suggested model discusses the problem of data forecasting.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006649","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 numerical study of the scattering in the He-Cu model with a Morse potential: Parabolic manifolds and exponentially small phenomena","authors":"","doi":"10.1016/j.cnsns.2024.108260","DOIUrl":"10.1016/j.cnsns.2024.108260","url":null,"abstract":"<div><p>We consider the classical approximation of a realistic model for the scattering of He atoms from Cu surfaces. For this problem, modeled by a two-degrees-of-freedom Hamiltonian system, the existence of chaos has been proven analytically very recently for sufficiently large values of the energy, if some quantity, known as the Stokes constant, is non-zero (Borondo et al., 2024). Taking two different and independent approaches, this paper provides numerical evidence that this is indeed the case. Both approaches provide the same value of the non-zero Stokes constant.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006838","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":"MHPD: An efficient evaluation method for influence maximization on hypergraphs","authors":"","doi":"10.1016/j.cnsns.2024.108268","DOIUrl":"10.1016/j.cnsns.2024.108268","url":null,"abstract":"<div><p>Influence maximization problem (IM) has been extensively applied in fields such as viral marketing, rumor control, and infectious disease prevention. However, research on the IM problem has primarily focused on ordinary networks, with limited attention devoted to hypergraphs. Firstly, we propose an efficient evaluation method, i.e., the multiple-hop probability dissemination method (MHPD), aiming to accurately and rapidly evaluate the propagation capacity of selected nodes. The MHPD method is a universal approach that is applicable to various network types, including hypergraphs, and it accommodates multiple probabilistic spreading models. Then, based on MHPD, we propose two novel algorithms for solving IM problem, i.e., MHPD-greedy and MHPD-heuristic. MHPD-greedy employs MHPD to evaluate the marginal benefits of nodes and iteratively adds nodes with the maximum marginal benefit to the seed set. MHPD-heuristic utilizes MHPD to evaluate the propagation capacity of each node and select the top-<span><math><mi>K</mi></math></span> nodes as the seeds. Experimental results on eight real-world hypergraphs and eight synthetic hypergraphs demonstrate that MHPD is capable of achieving near-identical accuracy in evaluating the propagation capability of both individual nodes and seed sets, while only incurring an average time overhead of merely <strong>0.25 %</strong> compared to Monte Carlo method. In comparison with seven cutting-edge algorithms, MHPD-heuristic demonstrates superior solution accuracy. Notably, MHPD-greedy maintains <strong>98.81 %</strong> of the solution accuracy while requiring only <strong>0.11 %</strong> of the time cost compared to the Greedy method. Furthermore, MHPD-greedy achieves an average performance improvement of <strong>23.4 %</strong> over the best baseline algorithm.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020702","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":"Maximum-correntropy-based sequential method for fast neural population activity reconstruction in the cortex from incomplete abnormally-disturbed noisy measurements","authors":"","doi":"10.1016/j.cnsns.2024.108266","DOIUrl":"10.1016/j.cnsns.2024.108266","url":null,"abstract":"<div><p>This paper continues to explore the membrane potential reconstruction and pattern recognition problem in a neural tissue modeled by Stochastic Dynamic Neural Field (SDNF) equation. Although recent research has suggested an efficient solution based on the state-space approach through nonlinear Bayesian filtering framework, it is becoming extremely difficult to ignore the existence of non-Gaussian uncertainties in the SDNFs as well as the stability problem of neuronal population dynamics to outliers. Motivated by recent events in signal processing and mathematical neuroscience, this paper explores the SDNFs in a presence of non-Gaussian uncertainties, which is the shot noise case, where the corrupted data might appear due to broken sensors. We derive the “distributionally robust” state estimator for the membrane potential reconstruction process that is the Maximum Correntropy Criterion Extended Kalman Filter (MCC-EKF) as well as its fast and numerically robust (to roundoff) implementation method by using the sequential principle of processing the measurement vectors. The numerical experiments are provided to illustrate the performance of the novel estimation methods.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985052","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":"Unconditional MBP preservation and energy stability of the stabilized exponential time differencing schemes for the vector-valued Allen–Cahn equations","authors":"","doi":"10.1016/j.cnsns.2024.108271","DOIUrl":"10.1016/j.cnsns.2024.108271","url":null,"abstract":"<div><p>The vector-valued Allen–Cahn equations have been extensively applied to simulate the multiphase flow models. In this paper, we consider the maximum bound principle (MBP) and corresponding numerical schemes for the vector-valued Allen–Cahn equations. We firstly formulate the stabilized equations via utilizing the linear stabilization technique, and then focus on the bounding constant of the nonlinear function based on the fact that the extremes of a constrained problem will occur in the bounded and convex domain. Later the first- and second-order stabilized exponential time differencing schemes are adopted for temporal integration, which are linear and unconditionally preserve the discrete MBP in the time discrete sense. Moreover, the proposed schemes can be proven to dissipate the original energy instead of the modified energy. Their convergence analysis is also presented. Various numerical examples in two and three dimensions are performed to verify these theoretical results and demonstrate the efficiency of the proposed schemes.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142039805","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":"Exponential control-based fixed/preassigned-time synchronization of output-coupled spatiotemporal networks with directed topology","authors":"","doi":"10.1016/j.cnsns.2024.108267","DOIUrl":"10.1016/j.cnsns.2024.108267","url":null,"abstract":"<div><p>This paper mainly explores the fixed-time and preassigned-time output synchronization of spatiotemporal networks with directed topology. Firstly, a kind of exponential-type control scheme associated with output feedback is developed. Subsequently, several sufficient criteria are established to ensure fixed-time output synchronization by utilizing the Lyapunov method and Taylor expansion. Moreover, the upper bound of convergence time is evaluated based on fixed-time stability theory. Furthermore, the preassigned-time output synchronization criteria are proposed by improving the fixed-time output controller, which incorporates a specified time parameter. Unlike previous forms, there are no stringent requirements imposed on the output matrix, whether semi-positive, non-singular or full rank in terms of columns. Finally, corresponding simulations are given to confirm the theoretical analysis.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141978985","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":"Variable-step L1 method combined with time two-grid algorithm for multi-singularity problems arising from two-dimensional nonlinear delay fractional equations","authors":"","doi":"10.1016/j.cnsns.2024.108270","DOIUrl":"10.1016/j.cnsns.2024.108270","url":null,"abstract":"<div><p>In this paper, we focus on the numerical simulation for two-dimensional nonlinear fractional sub-diffusion equations in the presence of time delay. Firstly, we investigate the existence, uniqueness and regularity of the solution for such problems. The theoretical result implies that the solution at <span><math><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> is smoother than that at <span><math><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math></span>, where <span><math><mi>τ</mi></math></span> is a constant time delay, and this is an improvement for the work (Tan et al., 2022). Secondly, a high-order difference scheme based on <span><math><mrow><mi>L</mi><mn>1</mn></mrow></math></span> method is constructed. For the sake of repairing the convergence order in temporal direction and improving the computational efficiency, an efficient time two-grid algorithm based on nonuniform meshes is first developed. The convergence order of the two-grid scheme reaches <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>F</mi></mrow><mrow><mo>−</mo><mo>min</mo><mrow><mo>{</mo><mi>r</mi><mi>α</mi><mo>,</mo><mn>2</mn><mo>−</mo><mi>α</mi><mo>}</mo></mrow></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow><mrow><mo>−</mo><mo>min</mo><mrow><mo>{</mo><mn>2</mn><mi>r</mi><mi>α</mi><mo>,</mo><mn>4</mn><mo>−</mo><mn>2</mn><mi>α</mi><mo>}</mo></mrow></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span> represent the number of the fine and coarse grids respectively, while <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are the space-step sizes. Furthermore, stability and convergence analysis of the proposed scheme are carefully verified by energy method. Finally, numerical experiments are carried out to show the validity of theoretical statements.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141993766","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":"Singularity properties of the entropy in an enclosed system characterized by accumulated noise stochastic processes","authors":"","doi":"10.1016/j.cnsns.2024.108256","DOIUrl":"10.1016/j.cnsns.2024.108256","url":null,"abstract":"<div><p>Due to the irreversibility of processes in an enclosed system, the randomness in the system increases in time and can be represented by an accumulated noise stochastic process. In contrast to the thermodynamics theory, the analysis of the system is based on the information theory point of view. The system is defined by two states: a time state and a timeless state. Based on the central limit theorem, due to the additivity of the noise process, the time state is characterized by the time-dependent Gaussian stochastic process. In contrast to Shannon's theory, precise expressions for the probability density, information, and entropy functions of the random variables defining the time-dependent process are derived and analyzed for a finite, infinite, and zero value of the related time-dependent variance. It has been proven that the entropy rate is not necessarily inversely proportional to time, as presented in previous works. Furthermore, mathematical proofs are presented, showing that the system entropy is a singularity function that increases towards infinity in the time state and then drops to zero value when the system enters the timeless state. The timeless state is characterized by the undefined pdf function, infinite values of information, and zero entropy.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424004416/pdfft?md5=48e3c53a32d4594436e281f7eeb84951&pid=1-s2.0-S1007570424004416-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141964576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}