Dynamics of a Periodically Pulsed Bio-reactor Model with a Hydraulic Storage Zone

In this talk we present a joint work with Feng-Bin Wang and Xiaoqiang Zhao. The work concerns with a periodically pulsed bio-reactor model of a flowing water habitat with a hydraulic storage zone in which no flow occurs. The full system can be reduced to a limiting system based on a conservation principle. Then we obtain sufficient conditions in terms of principal eigenvalues for the persistence of single population and the coexistence of two competing populations for the limiting system by appealing to the theory of monotone dynamical systems. Finally, we use the theory of chain transitive sets to lift the dynamics of the limiting system to the full system.