一类具有双时滞效应的氮–磷–浮游植物模型的动力学研究
Dynamic Analysis of a Nitrogen-Phosphorus-Plankton Model with Two Time Delays
DOI: 10.12677/AAM.2018.78128, PDF,  被引量    国家自然科学基金支持
作者: 赵潘：温州大学，浙江 温州
关键词: 营养；浮游植物；时滞；稳定性；Hopf分支；Nutrient； Phytoplankton； Delay； Stability； Hopf Bifurcation
摘要: 在水体富营养化的预防和控制的研究背景下，本论文构建了一类具有双时滞效应的氮–磷–浮游植物动力学模型，并对其相关动力学性质进行理论分析和数值仿真，解析出模型正平衡点具有局部渐近稳定性和发生Hopf分支的阈值条件，模拟出营养及浮游植物密度和Hopf分岔的动态演化过程。本论文的研究结果有利于从动力学的角度揭示营养与浮游植物之间的互作机制，有助于深入分析时滞效应对海洋生态系统的影响，为进一步预防和控制水体富营养化提供一定的理论支撑。
Abstract: Under the framework of water eutrophication prevention and control research, a nitro-gen-phosphorus-phytoplankton model with two delays will be investigated mathematically and numerically. Mathematical works have comprehensively explored the locally asymptotic stability of positive equilibrium and the threshold conditions of occurring Hopf bifurcation. Numerical si-mulation works have depicted the dynamic evolution process of nutrient and phytoplankton den-sity and Hopf bifurcation. These results provide a great help for the interaction between nutrition and phytoplankton in dynamics, and are helpful to deeply understand how the delay affects the dynamic trend of the marine ecosystem. Furthermore, they can provide certain theoretical support for further prevention and control of eutrophication of water bodies as well.
文章引用：赵潘. 一类具有双时滞效应的氮–磷–浮游植物模型的动力学研究[J]. 应用数学进展, 2018, 7(8): 1105-1118. https://doi.org/10.12677/AAM.2018.78128

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