季节性对藻类水华影响的建模研究.doc

季节性对藻类水华影响的建模研究 王稳地 西南大学数学与统计学院，重庆　 400715 摘要：本文建立了一个数学模型以模拟湖中藻类生长的动力学性态。模型引入了温度和阳光辐 射的季节性以分析气候波动的影响。论文证明了藻类基本再生率是无藻类演化状态全局稳定和 藻类持续生存的临界值。通过数值计算发现了温度分布的异质性加速藻类水华。还研究了如何 通过减少营养输入，打捞藻类和调水来控制水华的途径。这为水华的最优控制提供了理论基 础。 关键词：周期；临界值；稳定性；持续生存；温度 中图分类号： 029 Modeling seasonal e?ect on algae bloom Wendi Wang School of Mathematics and Statistics, Southwest University, Chongqing 400715 Abstract: A mathematical model is proposed to simulate dynamics of algae growth in a lake. Seasonal e?ects of temperature and solar radiation are incorporated to analyze in?uences of weather ?uctuations. It is shown that the reproductive ratio of algae is the threshold value between the global stability of the algae-free state and the persistence of algae blooms. It is found by numerical computations that the time heterogeneity of temperature accelerates the algae blooming. It is demonstrated by numerical simulations how the reduction of nutrient input, removal of algae and exchanging water can prevent the occurrence of algae blooming, which provides a theoretic basis for the optimal control of algae blooms. Key words: periodic; threshold; stability; persistence; temperature 1 Introduction Harmful algal blooms (HABs) threaten human health and produce deleterious consequences for other organisms in the aquatic ecosystem. For example, an estimated 105 ? 106 large ?sh could be killed in single events of HABs in in western Texas [1]. The control of algae blooms is crucially dependent upon the mechanisms of HABs formations. Mathematical models have served useful purposes to identify and quantify the processes contributing to bloom formations [1, 2]. Truscott and Brindley [3] formulated the system of phytoplankton and zooplankton where zooplankton strongly control the initiation of blooms. Notice that algae may produce 基金项目： Fund of Chinese Education Minister for PhD Supervisor (20100182110003)，NSF of China 作者简介： Wendi Wang（1957-），male，professor，major research direction：Mathematical Biology.