总磷限制下的藻类种群生长动态建模及稳定性研究

Algae Population Growth Dynamic Modeling and Stability Analysis under Phosphorus Limitation

摘要: 基于亚热带水库水体富营养化研究进程，本论文在动态建模过程中引入分布时滞来刻画水域生态系统中的时间延迟现象，构建了一类总磷限制下的藻类种群生长动态模型，对所建生态模型进行了一定的理论分析，建立了该生态模型边界平衡点渐近稳定的判断准则，明确了该生态模型具有这些特定动力学性态的一些关键参数阈值条件，这些研究工作为进一步预测吴家园水库营养盐动态演化趋势和揭示水域优势藻类种群生长动态规律提供了一定的理论基础。

Abstract: In this paper, firstly, on the basis of research progress of water eutrophication in subtropical reservoirs, the distributed delay is introduced to characterize time delay phenomenon of aquatic ecosystem in the process of algae population growth dynamic modeling, an algae population growth dynamic model under the restriction of total phosphorus has been structured. Secondly, some theoretical analysis on the ecological model have been investigated to establish some judgment criterions for the asymptotic stability of the boundary equilibrium points and define some critical parameter threshold conditions which can ensure that the ecological model has these specific dynamical states. Finally, these studies can provide certain theoretical basis for the further prediction of the nutrient dynamic evolution trend and the dominant algae population growth dynamic law in Wujiayuan reservoir.