{"title":"一类具有时滞的扩散植物wrack模型的动力学分析","authors":"Quanli Ji , Ranchao Wu , Biao Liu","doi":"10.1016/j.ecocom.2023.101050","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay.</p></div>","PeriodicalId":50559,"journal":{"name":"Ecological Complexity","volume":null,"pages":null},"PeriodicalIF":3.1000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamical analysis of a diffusion plant-wrack model with delay\",\"authors\":\"Quanli Ji , Ranchao Wu , Biao Liu\",\"doi\":\"10.1016/j.ecocom.2023.101050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay.</p></div>\",\"PeriodicalId\":50559,\"journal\":{\"name\":\"Ecological Complexity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ecological Complexity\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1476945X23000223\",\"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/S1476945X23000223","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}
Dynamical analysis of a diffusion plant-wrack model with delay
In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay.
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