Results in Applied Mathematics最新文献_第2页

Shared-endpoint correlations and hierarchy in random flows on graphs

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-13 DOI: 10.1016/j.rinam.2025.100549

Joshua Richland , Alexander Strang

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Singular bifurcations in a slow-fast modified Leslie-Gower model

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-12 DOI: 10.1016/j.rinam.2025.100558

Roberto Albarran-García , Martha Alvarez-Ramírez , Hildeberto Jardón-Kojakhmetov

{"title":"Singular bifurcations in a slow-fast modified Leslie-Gower model","authors":"Roberto Albarran-García , Martha Alvarez-Ramírez , Hildeberto Jardón-Kojakhmetov","doi":"10.1016/j.rinam.2025.100558","DOIUrl":"10.1016/j.rinam.2025.100558","url":null,"abstract":"<div><div>We study a predator–prey system with a generalist Leslie–Gower predator, a functional Holling type II response, and a weak Allee effect on the prey. The prey’s population often grows much faster than its predator, allowing us to introduce a small time scale parameter <span><math><mi>ɛ</mi></math></span> that relates the growth rates of both species, giving rise to a slow-fast system. Zhu and Liu (2022) show that, in the case of the weak Allee effect, Hopf singular bifurcation, slow-fast canard cycles, relaxation oscillations, etc. Our main contribution lies in the rigorous analysis of a degenerate scenario organized by a (degenerate) transcritical bifurcation. The key tool employed is the blow-up method that desingularizes the degenerate singularity. In addition, we determine the criticality of the singular Hopf bifurcation using recent intrinsic techniques that do not require a local normal form. The theoretical analysis is complemented by a numerical bifurcation analysis, in which we numerically identify and analytically confirm the existence of a nearby Takens–Bogdanov point.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100558"},"PeriodicalIF":1.4,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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An accurate collocation method for distributed order time fractional nonlinear diffusion wave equation with error analysis

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-11 DOI: 10.1016/j.rinam.2025.100556

M. Taghipour , H. Aminikhah

{"title":"An accurate collocation method for distributed order time fractional nonlinear diffusion wave equation with error analysis","authors":"M. Taghipour , H. Aminikhah","doi":"10.1016/j.rinam.2025.100556","DOIUrl":"10.1016/j.rinam.2025.100556","url":null,"abstract":"<div><div>The distributed-order fractional nonlinear diffusion-wave problem is a mathematical model that combines the concepts of fractional calculus and nonlinear diffusion-wave equations. It involves the use of distributed-order fractional operators, which generalize the traditional constant-order fractional operators by allowing the order of the derivative to vary over a range of values. This method works especially well for modeling complex systems whose behavior is affected by memory and nonlocal effects that happen across several scales. The objective of this article is to offer an appropriate numerical method for treating this problem. In order to achieve this, we dealt with the integral terms in the main equation using the Newton–Cotes quadrature rule. The problem reduces to a nonlinear system of equations through the computation of operational matrices. With the Levenberg–Marquardt algorithm as an option, the resulting system had been solved using Matlab’s fsolve tool. The analysis of the scheme and the function approximation have been thoroughly covered. Some test problem provided to compare the method with existing one. Additionally, the effect of collocation points on the numerical solution’s accuracy has been investigated.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100556"},"PeriodicalIF":1.4,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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On the numerical solution of a parabolic Fredholm integro-differential equation by the RBF method

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-10 DOI: 10.1016/j.rinam.2025.100559

Ihor Borachok, Roman Chapko, Oksana Palianytsia

{"title":"On the numerical solution of a parabolic Fredholm integro-differential equation by the RBF method","authors":"Ihor Borachok, Roman Chapko, Oksana Palianytsia","doi":"10.1016/j.rinam.2025.100559","DOIUrl":"10.1016/j.rinam.2025.100559","url":null,"abstract":"<div><div>This paper presents the numerical solution of an initial boundary value problem for a parabolic Fredholm integro-differential equation (FIDE) in bounded 2D and 3D spatial domains. To reduce the dimensionality of the problem, we employ the Laguerre transformation and Rothe’s method, with both first- and second-order time discretization approximations. As a result, the time-dependent problem is transformed into a recurrent sequence of boundary value problems for elliptic FIDEs. The radial basis function (RBF) method is then applied, where each stationary solution is approximated as a linear combination of radial basis functions centered at specific points, along with polynomial basis functions. The placement of these center points is outlined for both two-dimensional and three-dimensional regions. Collocation at center points generates a sequence of linear systems with integral coefficients. To compute these coefficients numerically, parameterization is performed, and Gauss–Legendre and trapezoidal quadratures are used. The shape parameter of the RBFs is optimized through a real-coded genetic algorithm. Numerical results in both two-dimensional and three-dimensional domains confirm the effectiveness and applicability of the proposed approaches.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100559"},"PeriodicalIF":1.4,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Minimum VaR and minimum CVaR optimal portfolios: The case of singular covariance matrix

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-08 DOI: 10.1016/j.rinam.2025.100557

Mårten Gulliksson , Stepan Mazur , Anna Oleynik

引用次数: 0

Analysis of Gaussian vs. Triangular Profiles for traffic flow modeling

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-08 DOI: 10.1016/j.rinam.2025.100555

Ghada A. Ahmed, Reem Algethamie

{"title":"Analysis of Gaussian vs. Triangular Profiles for traffic flow modeling","authors":"Ghada A. Ahmed, Reem Algethamie","doi":"10.1016/j.rinam.2025.100555","DOIUrl":"10.1016/j.rinam.2025.100555","url":null,"abstract":"<div><div>The present work provides a comprehensive comparative analysis between two advanced traffic density profiles — the Enhanced Gaussian Profile with Dynamic skewness and sigmoidal Spread, and the Novel Modified Triangular Profile with Interacting Peaks and Adaptive Heights — within the framework of the fractional Lighthill–Whitham–Richards (FLWR), which is an extension of the classical LWR model (Lighthill and Whitham, 1955; Richards, 1956; Sun and Zhang, 2011). The improved Gaussian Profile includes time-dependent skewness and spread, allowing it to dynamically adapt to changes in traffic conditions. On the other hand, the Modified Triangular Profile represents complex interactions between several congestion peaks (Newell, 1993; Treiber et al., 2000), similar to the multi-peak congestion phenomenon (Helbing, 2001; Kerner, 2004). The Von Neumann Stability Analysis (von Neumann and Richtmyer, 1950; von Neumann and Richtmyer, 1947) is employed and applied to both profiles to assess their stability under various traffic scenarios, providing valuable insights into the conditions under which each model remains robust.</div><div>We conducted a comparison between simulated traffic density data and real-world measurements to evaluate the accuracy and applicability of each profile. Our findings reveal a significant disparity in how these profiles capture small differences in traffic flow, particularly in situations that involve sudden changes in traffic patterns or external factors like weather conditions. This study not only enhances our understanding of traffic density modeling but also offers a framework for selecting acceptable traffic profiles based on specific real-world scenarios. The findings are essential for enhancing traffic management systems and designing more effective road networks (Richards, 1956; Mainardi, 2010; van der Houwen and Gijzen, 2010).</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100555"},"PeriodicalIF":1.4,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Wallach’s ratio principle under affine representation

IF 1.4

Results in Applied Mathematics Pub Date : 2025-03-06 DOI: 10.1016/j.rinam.2025.100554

Eszter Gselmann

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Analysis of positive solutions for classes of Laplacian systems with sign change weight functions and nonlinear boundary conditions

IF 1.4

Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100525

A. Shabanpour, S.H. Rasouli

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(2+1)-dimensional discrete exterior discretization of a general wave model in Minkowski spacetime

IF 1.4

Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100528

Sanna Mönkölä, Jukka Räbinä, Tytti Saksa, Tuomo Rossi

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Blow-up Whitney forms, shadow forms, and Poisson processes

IF 1.4

Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100529

Yakov Berchenko-Kogan , Evan S. Gawlik

{"title":"Blow-up Whitney forms, shadow forms, and Poisson processes","authors":"Yakov Berchenko-Kogan , Evan S. Gawlik","doi":"10.1016/j.rinam.2024.100529","DOIUrl":"10.1016/j.rinam.2024.100529","url":null,"abstract":"<div><div>The Whitney forms on a simplex <span><math><mi>T</mi></math></span> admit high-order generalizations that have received a great deal of attention in numerical analysis. Less well-known are the <em>shadow forms</em> of Brasselet, Goresky, and MacPherson. These forms generalize the Whitney forms, but have rational coefficients, allowing singularities near the faces of <span><math><mi>T</mi></math></span>. Motivated by numerical problems that exhibit these kinds of singularities, we introduce degrees of freedom for the shadow <span><math><mi>k</mi></math></span>-forms that are well-suited for finite element implementations. In particular, we show that the degrees of freedom for the shadow forms are given by integration over the <span><math><mi>k</mi></math></span>-dimensional faces of the <em>blow-up</em> <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span> of the simplex <span><math><mi>T</mi></math></span>. Consequently, we obtain an isomorphism between the cohomology of the complex of shadow forms and the cellular cohomology of <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>, which vanishes except in degree zero. Additionally, we discover a surprising probabilistic interpretation of shadow forms in terms of Poisson processes. This perspective simplifies several proofs and gives a way of computing bases for the shadow forms using a straightforward combinatorial calculation.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100529"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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