Abstract

A new nonlinear dynamics model of alga-aquatic animal is proposed based on the water ecosystem of Three Gorges Reservoir Area. The stability of the equilibria and Hopf bifurcation of the delay are studied. The results of the analysis show that with the increasing of the delay, the stability switch of the positive equilibrium and the asymptotically stable positive periodic solution resulting from Hopf bifurcation will occur. Thus, the time lag is one of the reasons that water quality is fluctuating in the water ecosystem of Three Gorges Reservoir Area, which may provide a theoretical basis for the oscillation of water quality.

Key words: Hopf bifurcation, delay, stability switch, water ecosystem.