{"title":"响应各种功能响应的动态行为变化:浮游生物系统的时空特征","authors":"Randhir Singh Baghel","doi":"10.1007/s40995-023-01413-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we focus on the comparison between ratio-dependent and Holling type-II functional response in the phytoplankton dynamics with the susceptible and infected populations with or without diffusion. The dynamics are investigated in terms of local stability using both the response function for the systems and the definition of the Hopf-bifurcation, which has been demonstrated to occur in the Holling type-II functional response using the half-saturation time (i.e. <span>\\(\\alpha\\)</span>) as the bifurcation parameter. We observed that the system’s dynamical behaviour is affected by the response functions and the system is more stable in the case of the ratio-dependent functional response. Furthermore, the study of higher-order perturbation terms reveals the heterogeneity of in-homogeneous spatiotemporal perturbation around temporal steady state outside the linear regime. The system behaviours to both types of response functions are studied numerically in the temporal and spatiotemporal domain (i.e. pattern formation in the diffusive population). Numerical simulation is used to examine the results.</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"47 2","pages":"445 - 455"},"PeriodicalIF":1.4000,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Dynamical Behaviour Changes in Response to Various Functional Responses: Temporal and Spatial Plankton System\",\"authors\":\"Randhir Singh Baghel\",\"doi\":\"10.1007/s40995-023-01413-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we focus on the comparison between ratio-dependent and Holling type-II functional response in the phytoplankton dynamics with the susceptible and infected populations with or without diffusion. The dynamics are investigated in terms of local stability using both the response function for the systems and the definition of the Hopf-bifurcation, which has been demonstrated to occur in the Holling type-II functional response using the half-saturation time (i.e. <span>\\\\(\\\\alpha\\\\)</span>) as the bifurcation parameter. We observed that the system’s dynamical behaviour is affected by the response functions and the system is more stable in the case of the ratio-dependent functional response. Furthermore, the study of higher-order perturbation terms reveals the heterogeneity of in-homogeneous spatiotemporal perturbation around temporal steady state outside the linear regime. The system behaviours to both types of response functions are studied numerically in the temporal and spatiotemporal domain (i.e. pattern formation in the diffusive population). Numerical simulation is used to examine the results.</p></div>\",\"PeriodicalId\":600,\"journal\":{\"name\":\"Iranian Journal of Science and Technology, Transactions A: Science\",\"volume\":\"47 2\",\"pages\":\"445 - 455\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2023-01-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iranian Journal of Science and Technology, Transactions A: Science\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40995-023-01413-x\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-023-01413-x","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Dynamical Behaviour Changes in Response to Various Functional Responses: Temporal and Spatial Plankton System
In this paper, we focus on the comparison between ratio-dependent and Holling type-II functional response in the phytoplankton dynamics with the susceptible and infected populations with or without diffusion. The dynamics are investigated in terms of local stability using both the response function for the systems and the definition of the Hopf-bifurcation, which has been demonstrated to occur in the Holling type-II functional response using the half-saturation time (i.e. \(\alpha\)) as the bifurcation parameter. We observed that the system’s dynamical behaviour is affected by the response functions and the system is more stable in the case of the ratio-dependent functional response. Furthermore, the study of higher-order perturbation terms reveals the heterogeneity of in-homogeneous spatiotemporal perturbation around temporal steady state outside the linear regime. The system behaviours to both types of response functions are studied numerically in the temporal and spatiotemporal domain (i.e. pattern formation in the diffusive population). Numerical simulation is used to examine the results.
期刊介绍:
The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences