赤潮藻类非线性动力学模型的分岔及稳定性研究

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,并发现了该模型通过准周期分岔产生混沌．

Stability and Bifurcation Behaviors Analysis in a Nonlinear Harmful Algal Dynamical Model

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.