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

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.