{"title":"Dynamical bifurcation point of a stochastic single-species model","authors":"Qingyang Hu, Jingliang Lv, Xiaoling Zou","doi":"10.1016/j.aml.2025.109596","DOIUrl":null,"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":2.8000,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925001466","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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 to the equation, the sign of 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.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.