{"title":"About stability of a mathematical model of Glassy-winged Sharpshooter population under Poisson’s jumps","authors":"Leonid Shaikhet","doi":"10.1016/j.aml.2025.109523","DOIUrl":null,"url":null,"abstract":"<div><div>The known mathematical model of Glassy-winged Sharpshooter, described by a nonlinear differential equation with delay, is considered under a combination of stochastic perturbations of the type of white noise and Poisson’s jumps. It is assumed that stochastic perturbations are directly proportional to the deviation of the system state from the positive equilibrium. Via the general method of Lyapunov functionals construction two different conditions for stability in probability of the model equilibrium are obtained. Numerical simulations and figures illustrate the obtained results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109523"},"PeriodicalIF":2.8000,"publicationDate":"2025-07-01","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/S0893965925000734","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/28 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The known mathematical model of Glassy-winged Sharpshooter, described by a nonlinear differential equation with delay, is considered under a combination of stochastic perturbations of the type of white noise and Poisson’s jumps. It is assumed that stochastic perturbations are directly proportional to the deviation of the system state from the positive equilibrium. Via the general method of Lyapunov functionals construction two different conditions for stability in probability of the model equilibrium are obtained. Numerical simulations and figures illustrate the obtained 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.
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