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Mathematical Methods in the Applied Sciences最新文献

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Nonlinear dynamics in a fear‐driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting 恐惧驱动的捕食者-猎物系统的非线性动力学：双稳态、分岔、九头蛇效应和最优收获
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10431
Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava
{"title":"Nonlinear dynamics in a fear‐driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting","authors":"Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava","doi":"10.1002/mma.10431","DOIUrl":"https://doi.org/10.1002/mma.10431","url":null,"abstract":"The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores optimal harvesting. We assume that the reproduction rate of prey is reduced due to the fear effect, and generalist predator follows Holling type II foraging strategy for predation. Additionally, we assume that predators are commercially valuable and harvested proportionately to their density. We demonstrate the existence of equilibrium points, their local and global stability, and bifurcation analysis. We observe that the model system undergoes a sequence of codimension one and codimension two bifurcations. Our results show that in the absence of predator harvesting, increasing levels of fear destabilize the predator–prey system, and controlled harvesting is beneficial for the coexistence of both populations. Also, the harvesting of predators may produce hydra and multiple hydra effects. We identify different types of bistability phenomena, which emphasize the importance of initial population size. Further, an optimal harvesting policy is also explored by formulating an optimal control problem (OCP). The harvesting cost‐functional is designed by incorporating the bionomic equilibrium state. We use Pontryagin's maximum principle and solve the OCP numerically. It is observed that implementing optimal harvesting not only contributes to the ecological benefits by maintaining a sustainable balance of predator–prey evolution but also plays a significant role in maximizing the economic benefits.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp estimates of solution of an elliptic problem on a family of open non‐convex planar sectors 开放非凸平面扇形族上椭圆问题解法的锐估计
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10449
Abdelaziz Douah, Abdelkader Tami, Mounir Tlemcani
{"title":"Sharp estimates of solution of an elliptic problem on a family of open non‐convex planar sectors","authors":"Abdelaziz Douah, Abdelkader Tami, Mounir Tlemcani","doi":"10.1002/mma.10449","DOIUrl":"https://doi.org/10.1002/mma.10449","url":null,"abstract":"Based on partial Fourier series analysis, we adapt on a model case a new approach to classical results obtained in the literature describing the singularities of a family a solutions of a second‐order elliptic problems on open non‐convex planar sectors. The method allows the exhibition of singular and regular frequencies, explicit decomposition, and description of coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter are obtained via this method. They are not uniform near where corners have opening angle generating a jump of singularity in Sobolev exponent, contrarily to the results obtained for harmonic and/or biharmonic problems on a family of convex planar sectors.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global solvability for semidiscrete Kirchhoff equation 半离散基尔霍夫方程的全局可解性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10453
Fumihiko Hirosawa
{"title":"Global solvability for semidiscrete Kirchhoff equation","authors":"Fumihiko Hirosawa","doi":"10.1002/mma.10453","DOIUrl":"https://doi.org/10.1002/mma.10453","url":null,"abstract":"It is effective to consider discretized problems for partial differential equations that are difficult to analyze themselves. The global solvability of the initial value problem of the Kirchhoff equation is still unsolved except in cases where the initial value is a specially restricted class. In this paper, we prove the global solvability of the semidiscrete Kirchhoff equation, which is obtained by discretizing the Kirchhoff equation with respect to spatial variables.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distributed order hantavirus model and its nonstandard discretizations and stability analysis 分布式阶梯汉坦病毒模型及其非标准离散化和稳定性分析
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10442
Mehmet Kocabiyik, Mevlüde Yakit Ongun
{"title":"Distributed order hantavirus model and its nonstandard discretizations and stability analysis","authors":"Mehmet Kocabiyik, Mevlüde Yakit Ongun","doi":"10.1002/mma.10442","DOIUrl":"https://doi.org/10.1002/mma.10442","url":null,"abstract":"It is crucial to understand the effects of deadly viruses on humans in advance. One such virus is the infectious hantavirus. Since the effects of viruses vary under different conditions, this study models the virus using distributed order differential equations. Because distributed order differential equations effectively capture variable effects in different conditions through the incorporated density function, this study aims to achieve a solution via the discretization method after presenting the equation system. A nonstandard finite difference scheme (NSFD) is used for the discretization. Then the stability analysis of the discretized system is investigated.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering 应用切利什科夫小波和最小二乘支持向量回归求解光学和工程学中出现的分数微分方程
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10420
Yadollah Ordokhani, Sedigheh Sabermahani, Parisa Rahimkhani
{"title":"Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering","authors":"Yadollah Ordokhani, Sedigheh Sabermahani, Parisa Rahimkhani","doi":"10.1002/mma.10420","DOIUrl":"https://doi.org/10.1002/mma.10420","url":null,"abstract":"Fractional‐order ray equations and fractional Duffing‐van der Pol oscillator equations are relationships utilized as a reliable means of modeling some phenomena in optics and engineering. The main motivation of this study is to introduce a new hybrid technique utilizing Chelyshkov wavelets and least squares‐support vector regression (LS‐SVR) for determining the approximate solution of fractional ray equations and fractional Duffing‐van der Pol oscillator equations (D‐v POEs). With the help of the Riemann‐Liouville operator for Chelyshkov wavelets and LS‐SVR (called Chw‐Ls‐SVR), the mentioned problems transform into systems of algebraic equations. The convergence analysis is discussed. Finally, the numerical results are proposed and compared with some schemes to display the capability of the numerical technique proposed here.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space 端点临界特里贝尔-利佐尔金空间中欧拉方程解的持久性
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI: 10.1002/mma.10443
JunSeok Hwang, Hee Chul Pak
{"title":"Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space","authors":"JunSeok Hwang, Hee Chul Pak","doi":"10.1002/mma.10443","DOIUrl":"https://doi.org/10.1002/mma.10443","url":null,"abstract":"Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space with is clarified.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Curves defined by a class of discrete operators: Approximation result and applications 一类离散算子定义的曲线：近似结果与应用
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-29 DOI: 10.1002/mma.10441
Rosario Corso, Gabriele Gucciardi
{"title":"Curves defined by a class of discrete operators: Approximation result and applications","authors":"Rosario Corso, Gabriele Gucciardi","doi":"10.1002/mma.10441","DOIUrl":"https://doi.org/10.1002/mma.10441","url":null,"abstract":"In approximation theory, classical discrete operators, like generalized sampling, Szász‐Mirak'jan, Baskakov, and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of curves by a class of discrete operators, and we exhibit graphical examples concerning several cases. The topic has useful implications about the computer graphics and the image processing: We discuss applications on the approximation and the reconstruction of curves in images.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions 再论周期波导：辐射条件、极限吸收原理和有界解空间
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-29 DOI: 10.1002/mma.10435
A. Kirsch, B. Schweizer
{"title":"Periodic waveguides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions","authors":"A. Kirsch, B. Schweizer","doi":"10.1002/mma.10435","DOIUrl":"https://doi.org/10.1002/mma.10435","url":null,"abstract":"We study the Helmholtz equation with periodic coefficients in a closed waveguide. A functional analytic approach is used to formulate and solve the radiation problem in a self‐contained exposition. In this context, we simplify the non‐degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied, and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Time delays in a double‐layered radial tumor model with different living cells 带有不同活细胞的双层径向肿瘤模型中的时间延迟
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-29 DOI: 10.1002/mma.10456
Yuanyuan Liu, Yuehong Zhuang
{"title":"Time delays in a double‐layered radial tumor model with different living cells","authors":"Yuanyuan Liu, Yuehong Zhuang","doi":"10.1002/mma.10456","DOIUrl":"https://doi.org/10.1002/mma.10456","url":null,"abstract":"This paper deals with the free boundary problem for a double‐layered tumor filled with quiescent cells and proliferating cells, where time delay in cell proliferation is taken into account. These two types of living cells exhibit different metabolic responses and consume nutrients at different rates and ( ). Time delay happens between the time at which a cell commences mitosis and the time at which the daughter cells are produced. The problem is reduced to a delay differential equation on the tumor radius over time, and the difficulty arises from the jump discontinuity of the consumption rate function. We give rigorous analysis on this new model and study the dynamical behavior of the global solutions for any initial .","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a parabolic equation in microelectromechanical systems with an external pressure 关于带有外部压力的微机电系统中的抛物线方程
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-28 DOI: 10.1002/mma.10427
Lingfeng Zhang, Xiaoliu Wang
{"title":"On a parabolic equation in microelectromechanical systems with an external pressure","authors":"Lingfeng Zhang, Xiaoliu Wang","doi":"10.1002/mma.10427","DOIUrl":"https://doi.org/10.1002/mma.10427","url":null,"abstract":"The parabolic problem on a bounded domain of with Dirichlet boundary condition models the microelectromechanical systems (MEMS) device with an external pressure term. In this paper, we classify the behavior of the solutions to this equation. We first show that under certain initial conditions, there exist critical constants and such that when , there exists a global solution, while for or , the solution quenches in finite time. The estimates of voltage , quenching time , and pressure term are investigated. The quenching set is proved to be a compact subset of with an additional condition on , provided is a convex bounded set. In particular, if is radially symmetric, then the origin is the only quenching point. Furthermore, we not only derive the two‐sided bound estimate for the quenching solution but also obtain its asymptotic behavior near the quenching time.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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