STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL  

作　　者：王洪礼 冯剑丰 沈菲 孙景 

机构地区：[1]Department of Mechanics and Engineering Measurement School of Mechanical Engineering

出　　处：《Applied Mathematics and Mechanics(English Edition)》2005年第6期729-734,共6页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10472077)the Science and Technology Development Project of Tianjin of China (No. 023111811)

摘　　要：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.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：harmful algal bloom population dynamics Hopf bifurcation normal form stability CHAOS 

分 类 号：Q948.1[生物学—植物学]