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Appl. Sci. 2016, 6(8), 221; doi:10.3390/app6080221

Global Dynamics of Modeling Flocculation of Microorganism

1
Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
2
Department of Biological Science and Technology, School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Academic Editor: Yang Kuang
Received: 31 May 2016 / Accepted: 26 July 2016 / Published: 5 August 2016
(This article belongs to the Special Issue Dynamical Models of Biology and Medicine)
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Abstract

From a biological perspective, a dynamic model describing the cultivation and flocculation of a microorganism that uses two different kinds of nutrients (carbon source and nitrogen source) is proposed. For the proposed model, there always exists a boundary equilibrium, i.e., R h o d o p s e u d o m o n a s p a l u s t r i s -free equilibrium. Furthermore, under additional conditions, the model also has five positive equilibria at most, i.e., the equilibria for which carbon source, nitrogen source, R h o d o p s e u d o m o n a s p a l u s t r i s and flocculants are coexistent. The phenomena of backward and forward bifurcations are extensively discussed by using center manifold theory. The global stability of the boundary equilibrium of the proposed model is deeply investigated. Moreover, the local stability of the positive equilibrium and the uniform persistence of the proposed model are discussed. Under additional conditions, the global stability of the positive equilibrium is studied. Some control strategies are given by the theoretical analysis. Finally, some numerical simulations are performed to confirm the correctness of the theoretical results. View Full-Text
Keywords: dynamic model; flocculation; global stability; uniform persistence dynamic model; flocculation; global stability; uniform persistence
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, W.; Ma, W.; Yan, H. Global Dynamics of Modeling Flocculation of Microorganism. Appl. Sci. 2016, 6, 221.

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