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

WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(6): 671-676

WANG Hong-li, FENG Jian-feng, SHEN Fei, SUN Jing. Stability and Bifurcation Behaviors Analysis in a Nonlinear Harmful Algal Dynamical Model[J]. Applied Mathematics and Mechanics, 2005, 26(6): 671-676.

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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

Received Date: 2003-05-10
Rev Recd Date: 2005-01-25
Publish Date: 2005-06-15

Abstract

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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References(6)

References

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