Impulsive control strategy for a chemostat model with nutrient recycling and distributed time-delay
Corresponding Author
Baodan Tian
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
Correspondence to: Baodan Tian, School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China.
E-mail: [email protected]
Search for more papers by this authorShouming Zhong
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
Search for more papers by this authorNing Chen
School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
Search for more papers by this authorXianqing Liu
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
Search for more papers by this authorCorresponding Author
Baodan Tian
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
Correspondence to: Baodan Tian, School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China.
E-mail: [email protected]
Search for more papers by this authorShouming Zhong
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
Search for more papers by this authorNing Chen
School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China
Search for more papers by this authorXianqing Liu
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China
Search for more papers by this authorAbstract
On the basis of the simplest and deterministic chemostat model, we introduce impulsive input, nutrient recycling, and distributed time-delay into the model in this paper. By using comparison theorem, Floquet theory, and small amplitude skills in the impulsive differential equation, it proves that if the period of impulsive input is too long and the parameter α of the kernel function in the delay is too small, then there exists a microorganism-eradication periodic solution that is globally asymptotically stable, and the cultivation of the microorganism fails. On the contrary, if we choose suitable impulsive strategy, such as increasing the concentration of the substrate or enhance the proportion of the concentration of the impulsive input of the substrate at periodic time to that for the microbial growth, then the system could be controlled to be permanent, and the cultivation of the microorganism will be successful. Copyright © 2013 John Wiley & Sons, Ltd.
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