{"title":"Stability analysis of a flocculation model incorporating cell size, time delay, and control","authors":"Dongdong Ni , Wanbiao Ma , Qinglai Wei","doi":"10.1016/j.aml.2024.109294","DOIUrl":null,"url":null,"abstract":"<div><p>The influence of algal cell size on nutrient absorption, and the time delay in reproduction is paramount in biological terms. Furthermore, the control is necessary during algal flocculation harvesting and sewage treatment. Therefore, we investigated the properties of a single cell algal flocculation model with time delay, size structure and control. First, we introduced a dimensionless model. Then, we analyzed the existence of positive equilibrium states and studied the equilibrium states of the model. Finally, the numerical simulation revealed that the model exhibits backward bifurcation.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109294"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-03","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/S0893965924003148","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
The influence of algal cell size on nutrient absorption, and the time delay in reproduction is paramount in biological terms. Furthermore, the control is necessary during algal flocculation harvesting and sewage treatment. Therefore, we investigated the properties of a single cell algal flocculation model with time delay, size structure and control. First, we introduced a dimensionless model. Then, we analyzed the existence of positive equilibrium states and studied the equilibrium states of the model. Finally, the numerical simulation revealed that the model exhibits backward bifurcation.
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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