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.

Key words: chaos, harmful algal bloom, population dynamics, Hopf bifurcation, normal form, stability