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September  2017, 16(5): 1883-1891. doi: 10.3934/cpaa.2017091

## Global dynamics of a microorganism flocculation model with time delay

 1 Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China 2 Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

* Corresponding author

Received  June 2016 Revised  March 2017 Published  May 2017

Fund Project: This work was supported by the China Scholarship Council, the Fundamental Research Funds for the Central Universities (FRF-BY-14-036) and the National Natural Science Foundation of China (11471034)

In this paper, we consider a microorganism flocculation model with time delay. In this model, there may exist a forward bifurcation/backward bifurcation. By constructing suitable positively invariant sets and using Lyapunov-LaSalle theorem, we study the global stability of the equilibria of the model under certain conditions. Furthermore, we also investigate the permanence of the model, and an explicit expression of the eventual lower bound of microorganism concentration is given.

Citation: Songbai Guo, Wanbiao Ma. Global dynamics of a microorganism flocculation model with time delay. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1883-1891. doi: 10.3934/cpaa.2017091
##### References:

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##### References:
Forward bifurcation.
Backward bifurcation.
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