Global dynamics of a microorganism flocculation model with time delay

Songbai Guo; Wanbiao Ma

doi:10.3934/cpaa.2017091

Article Contents

2017, Volume 16, Issue 5: 1883-1891. Doi: 10.3934/cpaa.2017091

This issue Previous Article Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region Next Article Dynamics of some stochastic chemostat models with multiplicative noise

Global dynamics of a microorganism flocculation model with time delay

Songbai Guo^1,2, and
Wanbiao Ma^1, ,

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
* Corresponding author

Received: June 2016

Revised: March 2017

Published: October 2017

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).

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Abstract

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.

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Mathematics Subject Classification: Primary: 92B05, 37N25; Secondary: 34K20, 34D23.

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Figure 1. Forward bifurcation.

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Figure 2. Backward bifurcation.

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