赤潮藻类非线性动力学模型的分岔及稳定性研究  

Stability and Bifurcation Behaviors Analysis in aNonlinear Harmful Algal Dynamical Model

作　　者：王洪礼[1] 冯剑丰[1] 沈菲[1] 孙景[1] 

机构地区：[1]天津大学机械工程学院力学系,天津300072

出　　处：《应用数学和力学》2005年第6期671-676,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10472077);天津市科技发展计划资助项目(023111811)

摘　　要：　选取两种常见赤潮藻类和一种浮游动物,考虑生态环境的富营养化及赤潮藻类与浮游动物的相互作用,建立了多种群赤潮藻类的非线性动力学模型·　首次运用现代非线性动力学理论,对模型的稳定性及分岔行为进行了研究·　得到了发生Hopf分岔时的分岔参数值,判断了极限环的稳定性。A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics,the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed.The result shows that through quasi_periodicity bifurcation the system is lost in chaos.

关 键 词：非线性动力学模型 稳定性研究 藻类 赤潮 非线性动力学理论 HOPF分岔 浮游动物 相互作用 富营养化 生态环境 分岔行为 周期分岔 多种群 参数值 极限环 

分 类 号：X55[环境科学与工程—环境工程] TQ450.1[化学工程—农药化工]