{"title":"双猎物-双捕食者模型的行为分析","authors":"Abhijit Jana , Sankar Kumar Roy","doi":"10.1016/j.ecocom.2021.100942","DOIUrl":null,"url":null,"abstract":"<div><p>To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.</p></div>","PeriodicalId":50559,"journal":{"name":"Ecological Complexity","volume":"47 ","pages":"Article 100942"},"PeriodicalIF":3.1000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ecocom.2021.100942","citationCount":"11","resultStr":"{\"title\":\"Behavioural analysis of two prey-two predator model\",\"authors\":\"Abhijit Jana , Sankar Kumar Roy\",\"doi\":\"10.1016/j.ecocom.2021.100942\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.</p></div>\",\"PeriodicalId\":50559,\"journal\":{\"name\":\"Ecological Complexity\",\"volume\":\"47 \",\"pages\":\"Article 100942\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.ecocom.2021.100942\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ecological Complexity\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1476945X21000350\",\"RegionNum\":3,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ecological Complexity","FirstCategoryId":"93","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1476945X21000350","RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECOLOGY","Score":null,"Total":0}
Behavioural analysis of two prey-two predator model
To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.
期刊介绍：
Ecological Complexity is an international journal devoted to the publication of high quality, peer-reviewed articles on all aspects of biocomplexity in the environment, theoretical ecology, and special issues on topics of current interest. The scope of the journal is wide and interdisciplinary with an integrated and quantitative approach. The journal particularly encourages submission of papers that integrate natural and social processes at appropriately broad spatio-temporal scales.
Ecological Complexity will publish research into the following areas:
• All aspects of biocomplexity in the environment and theoretical ecology
• Ecosystems and biospheres as complex adaptive systems
• Self-organization of spatially extended ecosystems
• Emergent properties and structures of complex ecosystems
• Ecological pattern formation in space and time
• The role of biophysical constraints and evolutionary attractors on species assemblages
• Ecological scaling (scale invariance, scale covariance and across scale dynamics), allometry, and hierarchy theory
• Ecological topology and networks
• Studies towards an ecology of complex systems
• Complex systems approaches for the study of dynamic human-environment interactions
• Using knowledge of nonlinear phenomena to better guide policy development for adaptation strategies and mitigation to environmental change
• New tools and methods for studying ecological complexity
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