Affiliation:
1. Department of Applied Mathematics School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083, P. R. China
2. College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao 266590, P. R. China
3. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology Shandong University of Science and Technology Qingdao 266590, P. R. China
Abstract
In this paper, we aim to propose a new chemostat model with continuous microbial culture and harvest, and to investigate the dynamics of the model. Different to the conventional ones, our model includes a constant periodic flocculant transmission. For the proposed system, by using theory of impulsive differential equations, we show that the microbe-extinction periodic solution is globally asymptotically stable when a threshold value is less than 1, and system is permanent when a certain threshold value is greater than 1. Then, according to the threshold associated with microbial extinction or existence, the control strategy for microbial continuous cultivation and harvest is discussed. Under such control strategy, continuous microbial culture and harvest can be achieved by adjusting input time, input amount or concentration of the flocculant. Finally, an example with numerical simulations is given to illustrate our theoretical conclusions.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology,Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology
Cited by
11 articles.
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