The Effect of Diffusion on the Dynamics of a Predator-Prey Chemostat Model
Hua Nie, Yao Shi, Jianhua Wu
Abstract
This paper deals with a diffusive predator-prey chemostat system which describes the growth of planktonic rotifers, Brachionus calyciflorus, feeding on unicellular green algae, Chlorella vulgaris. The dynamical behavior of this system is established in terms of the diffusion rate. The results show that there exist two critical diffusion rates which classify the dynamical behavior of this system into the following three scenarios: (i) for a large diffusion rate, all species will be washed out; (ii) for an intermediate diffusion rate, the predator goes extinct and the prey survives; (iii) for a small diffusion rate, all species coexist. Finally, our numerical results show that the solution of this system may undergo a steady-state bifurcation or Hopf bifurcation for a suitably small diffusion rate, which supplements our theoretical results.