赤潮藻类非线性动力学模型的分岔及稳定性研究

基金项目: 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)

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

Department of Mechanics and Engineering Measurement, School of Mechanical Engineering, Tianjin University, Tianjin 300072, P. R. China

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,并发现了该模型通过准周期分岔产生混沌．
- 赤潮 /
- 种群动力学 /
- Hopf分岔 /
- 正规型 /
- 稳定性 /
- 混沌
Abstract: 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.
- harmful algal bloom /
- population dynamics /
- Hopf bifurcation /
- normal form /
- stability /
- chaos

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