{"title":"Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response","authors":"M. Dawed, Kiros G. Kebedow","doi":"10.1111/nrm.12316","DOIUrl":null,"url":null,"abstract":"In this paper, we have discussed harvesting of prey and intermediate predator species. Both are subjected to Holling type I–V functional response. Conditions for local and global stability of the nonnegative equilibria are verified. The permanent coexistence criterion of the model system and existence of optimal equilibrium solution of the control problem are demonstrated. Maximum sustainable yield and maximal net present revenue are determined. To confirm analytical results, numerical solution has been carried out using the Matlab™ ODE solver ODE45 and the simulations show the model system reveals complex behavior (such as oscillations), which reflects the real situation.","PeriodicalId":49778,"journal":{"name":"Natural Resource Modeling","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/nrm.12316","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Natural Resource Modeling","FirstCategoryId":"93","ListUrlMain":"https://doi.org/10.1111/nrm.12316","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we have discussed harvesting of prey and intermediate predator species. Both are subjected to Holling type I–V functional response. Conditions for local and global stability of the nonnegative equilibria are verified. The permanent coexistence criterion of the model system and existence of optimal equilibrium solution of the control problem are demonstrated. Maximum sustainable yield and maximal net present revenue are determined. To confirm analytical results, numerical solution has been carried out using the Matlab™ ODE solver ODE45 and the simulations show the model system reveals complex behavior (such as oscillations), which reflects the real situation.
期刊介绍：
Natural Resource Modeling is an international journal devoted to mathematical modeling of natural resource systems. It reflects the conceptual and methodological core that is common to model building throughout disciplines including such fields as forestry, fisheries, economics and ecology. This core draws upon the analytical and methodological apparatus of mathematics, statistics, and scientific computing.
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