一类水体富营养化复杂动力系统构建及其动力学分析 Dynamics Analysis and Construction of a Water Eutrophication Complex Dynamical System

基于吴家园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式函数来刻画总磷输入随季度变化的特征，构建了一类水体富营养化复杂动力系统，对所建系统进行了一定的理论分析与数值模拟，建立了该系统内平衡点渐近稳定的判断准则，模拟出总磷浓度和藻类种群密度动态变化趋势，剖析出总磷与藻类种群之间的相互作用机制，进而揭示总磷输入可控策略对水体富营养化状况和藻类水华的影响作用机理。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探索吴家园水库藻类种群生长动态规律提供了一定的理论基础。 In this paper, firstly, on the basis of research progress of water eutrophication in Wujiayuan res-ervoir, a distributed function is introduced to characterize the total phosphorus input being changed with the season in the process of dynamic modeling, a water eutrophication complex dy-namical system has been structured. Secondly, some theoretical analysis and numerical simulation on the complex dynamical system have been investigated to establish some judgment criterions for the asymptotic stability of the internal equilibrium point and describe the dynamic trends of total phosphorus concentration and algal population density, which can dissect the interaction mechanism between total phosphorus and algal population, and then reveal the influence mecha-nism of total phosphorus input control strategy on eutrophication status and algal bloom. Finally, these studies can provide certain theoretical basis for the further prediction of the nutrient dy-namic evolution trend and the deep exploration of the algae population growth dynamic law in Wujiayuan reservoir.