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 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 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 suitably small diffusion rate, which supplements our theoretical results.

聂华，教授、博士生导师，长期从事反应扩散方程与空间生态种群模型的理论研究与数值模拟。现任中国数学会计算数学分会第十届委员会理事、陕西省计算数学学会第十届常务理事。2006年获得博士学位，2012年入选教育部“新世纪优秀人才支持计划”；2015年入选陕西省“青年科技新星”；多次赴美国明尼苏达大学、澳大利亚新英格兰大学、台湾清华大学合作研究与访问。主持国家自然科学基金项目4项，主持完成省部级项目3项；已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“SIAM J. Appl. Dyn. Syst.”、“J. Differential Equations”、“J. Math. Biol.”、“Math. Biosci.”、“European J. Appl. Math.”、“Proc. London Math. Soc.”、“Sci. China Math.”等国内外知名刊物上发表学术论文60多篇；在科学出版社出版专著2部。