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Dynamical bifurcation point of a stochastic single-species model 随机单物种模型的动力分岔点
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109596
Qingyang Hu, Jingliang Lv, Xiaoling Zou
{"title":"Dynamical bifurcation point of a stochastic single-species model","authors":"Qingyang Hu,&nbsp;Jingliang Lv,&nbsp;Xiaoling Zou","doi":"10.1016/j.aml.2025.109596","DOIUrl":"10.1016/j.aml.2025.109596","url":null,"abstract":"<div><div>A stochastic single-species model subject to additive Allee effects and nonlinear stochastic perturbation is proposed and analyzed. First we demonstrate that this model has a unique positive solution for any positive initial value. Then, by analyzing the stability of invariant measures, we testify that there is a unique dynamical bifurcation point <span><math><mi>Λ</mi></math></span> to the equation, the sign of <span><math><mi>Λ</mi></math></span> determines the dynamical properties of the equation, and the density function of the invariant measure can be expressed. In the end, numerical simulations are introduced to verify the theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109596"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106435","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}
引用次数: 0
Threshold of a stochastic single population system with infinite delay and time-varying coefficients 具有无限延迟和时变系数的随机单种群系统的阈值
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109597
Daipeng Kuang , Quanxin Zhu , Kai Liu
{"title":"Threshold of a stochastic single population system with infinite delay and time-varying coefficients","authors":"Daipeng Kuang ,&nbsp;Quanxin Zhu ,&nbsp;Kai Liu","doi":"10.1016/j.aml.2025.109597","DOIUrl":"10.1016/j.aml.2025.109597","url":null,"abstract":"<div><div>This paper focuses on a category of stochastic single population systems. Under mild assumptions, we provide a sufficient condition for the existence of stationary distribution in this system by employing variable substitution and the Krylov–Bogoliubov theorem. Furthermore, we demonstrate its proximity to being the sufficient and necessary condition by examining the system’s extinction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109597"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934865","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}
引用次数: 0
Local solution becomes global solution as damping coefficient goes to infinity 当阻尼系数趋于无穷时，局部解变为全局解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109599
Jiangbo Han , Caijun Wang , Runzhang Xu , Chao Yang
{"title":"Local solution becomes global solution as damping coefficient goes to infinity","authors":"Jiangbo Han ,&nbsp;Caijun Wang ,&nbsp;Runzhang Xu ,&nbsp;Chao Yang","doi":"10.1016/j.aml.2025.109599","DOIUrl":"10.1016/j.aml.2025.109599","url":null,"abstract":"<div><div>We consider a class of wave equations with strong damping, weak damping and nonlinear source term. By constructing the relationship between the blowup time and the coefficients of strong damping and weak damping, we exhibit and verify an interesting phenomenon that the local solution becomes the global solution as the coefficient of strong damping or weak damping goes to infinity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109599"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934864","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}
引用次数: 0
A novel integral inequality for stability of age-structured epidemic models 年龄结构流行病模型稳定性的一个新的积分不等式
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109598
Jianquan Li , Yuming Chen , Fengqin Zhang , Peijun Zhang
{"title":"A novel integral inequality for stability of age-structured epidemic models","authors":"Jianquan Li ,&nbsp;Yuming Chen ,&nbsp;Fengqin Zhang ,&nbsp;Peijun Zhang","doi":"10.1016/j.aml.2025.109598","DOIUrl":"10.1016/j.aml.2025.109598","url":null,"abstract":"<div><div>In this paper, based on a novel integral inequality and the Lyapunov direct method, we propose a systematic approach to determining the global stability of the endemic steady states of age-structured epidemic models. The inequality makes it convenient to verify the negative (semi-)definiteness of the derivative of a Lyapunov functional candidate. The applicability of this approach is illustrated with two age-structured SI and SEI models.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109598"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934766","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}
引用次数: 0
Supercloseness in a balanced norm of the NIPG method on Bakhvalov-type meshes for a reaction diffusion problem 反应扩散问题bakhvalov型网格NIPG方法平衡范数的超接近性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-09 DOI: 10.1016/j.aml.2025.109594
Jiayu Wang , Xiaowei Liu , Xiaoqi Ma
{"title":"Supercloseness in a balanced norm of the NIPG method on Bakhvalov-type meshes for a reaction diffusion problem","authors":"Jiayu Wang ,&nbsp;Xiaowei Liu ,&nbsp;Xiaoqi Ma","doi":"10.1016/j.aml.2025.109594","DOIUrl":"10.1016/j.aml.2025.109594","url":null,"abstract":"<div><div>For numerical methods applied to singularly perturbed reaction-diffusion problems, the balanced norm has emerged as an effective tool. In this manuscript, we analyze supercloseness properties in the balanced norm for the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. To achieve this, we construct a novel interpolant that combines the Lagrange interpolant and a local weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> projection. Furthermore, by appropriately defining penalty parameters at the nodal points of the Bakhvalov-type mesh, we establish supercloseness of almost order <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> in most cases.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109594"},"PeriodicalIF":2.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941938","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}
引用次数: 0
Solvability of a class of nonlinear system of difference equations with homogeneity 一类具有齐次性的非线性差分方程组的可解性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-09 DOI: 10.1016/j.aml.2025.109595
Stevo Stević
{"title":"Solvability of a class of nonlinear system of difference equations with homogeneity","authors":"Stevo Stević","doi":"10.1016/j.aml.2025.109595","DOIUrl":"10.1016/j.aml.2025.109595","url":null,"abstract":"<div><div>We show that the following nonlinear system of difference equations of interest <span><span><span><math><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mrow><mo>(</mo><mi>l</mi><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><mfrac><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>l</mi></mrow></msub><munderover><mrow><mo>∏</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>≠</mo><mi>l</mi></mrow><mrow><mi>k</mi></mrow></munderover><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></mrow></msubsup></mrow><mrow><mi>f</mi><mrow><mo>(</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>N</mi><mo>,</mo><mspace></mspace><mi>l</mi><mo>=</mo><mover><mrow><mn>1</mn><mo>,</mo><mi>k</mi></mrow><mo>¯</mo></mover><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow><mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></mrow></msubsup><mo>∈</mo><mi>ℂ</mi><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>,</mo></mrow></math></span> <span><math><mrow><mi>j</mi><mo>=</mo><mover><mrow><mn>1</mn><mo>,</mo><mi>k</mi></mrow><mo>¯</mo></mover><mo>,</mo></mrow></math></span> and the function <span><math><mrow><mi>f</mi><mo>:</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>→</mo><mi>ℂ</mi></mrow></math></span> is homogeneous of degree <span><math><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></math></span>, is solvable in a closed form considerably extending some results in the literature.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109595"},"PeriodicalIF":2.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934767","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}
引用次数: 0
Convergence rate of truncated EM method for periodic stochastic differential equations in superlinear scenario 超线性情况下周期随机微分方程的截短EM方法的收敛速度
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-29 DOI: 10.1016/j.aml.2025.109592
Yongmei Cai
{"title":"Convergence rate of truncated EM method for periodic stochastic differential equations in superlinear scenario","authors":"Yongmei Cai","doi":"10.1016/j.aml.2025.109592","DOIUrl":"10.1016/j.aml.2025.109592","url":null,"abstract":"<div><div>Periodicity has been widely recognised in a variety of areas including biology, finance and control theory. As an important class of non-autonomous SDEs, stochastic differential equations (SDEs) with periodic coefficients have thus been receiving great attention recently. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) method to the superlinear SDEs with periodic coefficients and generate an almost optimal convergence rate of order close to <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>. Due to the typical features of such SDEs including periodicity and super-linearity, this work becomes challenging and non-trivial. Finally our theory is demonstrated by computer simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109592"},"PeriodicalIF":2.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891294","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}
引用次数: 0
Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law 双曲齐次标量一维守恒律的显式解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-29 DOI: 10.1016/j.aml.2025.109593
Didier Clamond
{"title":"Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law","authors":"Didier Clamond","doi":"10.1016/j.aml.2025.109593","DOIUrl":"10.1016/j.aml.2025.109593","url":null,"abstract":"<div><div>A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scalar 1D equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mrow><mo>[</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>, for any flux <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> and initial condition <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> that are analytic. This formula is valid for some times <span><math><mrow><mi>t</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mi>u</mi></math></span> remaining analytic.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109593"},"PeriodicalIF":2.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891295","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}
引用次数: 0
Soliton solutions and strange wave solutions for (2＋1)-dimensional nonlocal nonlinear Schrödinger equation with PT-symmetric term 具有pt对称项的（2+1）维非局部非线性Schrödinger方程的孤子解和奇异波解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-27 DOI: 10.1016/j.aml.2025.109583
Jingwen Yu, Fajun Yu, Lei Li
{"title":"Soliton solutions and strange wave solutions for (2＋1)-dimensional nonlocal nonlinear Schrödinger equation with PT-symmetric term","authors":"Jingwen Yu,&nbsp;Fajun Yu,&nbsp;Lei Li","doi":"10.1016/j.aml.2025.109583","DOIUrl":"10.1016/j.aml.2025.109583","url":null,"abstract":"<div><div>In this paper, the fundamental (1＋1)-dimensional nonlinear Schrödinger equation is extended to a novel (2＋1)-dimensional nonlocal nonlinear Schrödinger (NNLS) equation with a PT-symmetric term. We obtain the 1-soliton solution, 2-soliton solution, breather wave and strange wave solution of the (2＋1)-dimensional NNLS equation via the Hirota bilinear method. Some obtained solutions describe the interactions between bright and breather waves propagating along the <span><math><mi>y</mi></math></span>-axis and long waves propagating along the <span><math><mi>x</mi></math></span>-axis. And the (2＋1)-dimensional NNLS equation has the PT-symmetry property and many conservation laws, it is worthy of being studied in nonlinear optics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109583"},"PeriodicalIF":2.9,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888089","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}
引用次数: 0
Analysis of a stochastic Alzheimer’s disease model with β-amyloid oligomer effect: Stationary distribution and extinction 具有β-淀粉样蛋白低聚物效应的随机阿尔茨海默病模型分析：平稳分布和消失
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-26 DOI: 10.1016/j.aml.2025.109581
Baoquan Zhou, Ningzhong Shi
{"title":"Analysis of a stochastic Alzheimer’s disease model with β-amyloid oligomer effect: Stationary distribution and extinction","authors":"Baoquan Zhou,&nbsp;Ningzhong Shi","doi":"10.1016/j.aml.2025.109581","DOIUrl":"10.1016/j.aml.2025.109581","url":null,"abstract":"<div><div><span><math><mi>β</mi></math></span>-amyloid (A<span><math><mi>β</mi></math></span>) oligomers have been increasingly shown to produce the crucial cytotoxicity during the progression of Alzheimer’s disease (AD). In this paper, we develop a stochastic AD model with A<span><math><mi>β</mi></math></span> oligomer effect, where Black–Karasinski process is introduced to describe the random fluctuations in neurobiological environment. First, the well-posedness and Markov–Feller property of the solution of the model are proved. By Lyapunov functional approach and stochastic stability theory, we establish sufficient conditions for the existence of a stationary distribution. Moreover, the exponential extinction of A<span><math><mi>β</mi></math></span> oligomers is provided.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109581"},"PeriodicalIF":2.9,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879157","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}
引用次数: 0
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