{"title":"Hopf bifurcation in delayed nutrient-microorganism model with network structure.","authors":"Mengxin Chen, Qianqian Zheng, Ranchao Wu, Liping Chen","doi":"10.1080/17513758.2021.2020915","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay <i>τ</i> as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such a random network nutrient-microorganism model. Noticing that the results of the direction of the Hopf bifurcation in a random network model are rare, we thus try to use the method of multiple time scales (MTS) to derive amplitude equation and determine the direction of the Hopf bifurcation. It is showed that the delayed random network nutrient-microorganism model can exhibit a supercritical or subcritical Hopf bifurcation. Numerical experiments are performed to verify the validity of the theoretical analysis.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":" ","pages":"1-13"},"PeriodicalIF":2.7000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Dynamics","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1080/17513758.2021.2020915","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECOLOGY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce and deal with the delayed nutrient-microorganism model with a random network structure. By employing time delay τ as the main critical value of the Hopf bifurcation, we investigate the direction of the Hopf bifurcation of such a random network nutrient-microorganism model. Noticing that the results of the direction of the Hopf bifurcation in a random network model are rare, we thus try to use the method of multiple time scales (MTS) to derive amplitude equation and determine the direction of the Hopf bifurcation. It is showed that the delayed random network nutrient-microorganism model can exhibit a supercritical or subcritical Hopf bifurcation. Numerical experiments are performed to verify the validity of the theoretical analysis.
期刊介绍：
Journal of Biological Dynamics, an open access journal, publishes state of the art papers dealing with the analysis of dynamic models that arise from biological processes. The Journal focuses on dynamic phenomena at scales ranging from the level of individual organisms to that of populations, communities, and ecosystems in the fields of ecology and evolutionary biology, population dynamics, epidemiology, immunology, neuroscience, environmental science, and animal behavior. Papers in other areas are acceptable at the editors’ discretion. In addition to papers that analyze original mathematical models and develop new theories and analytic methods, the Journal welcomes papers that connect mathematical modeling and analysis to experimental and observational data. The Journal also publishes short notes, expository and review articles, book reviews and a section on open problems.
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