Premium
Impulsive control strategy for a chemostat model with nutrient recycling and distributed time‐delay
Author(s) -
Tian Baodan,
Zhong Shouming,
Chen Ning,
Liu Xianqing
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2807
Subject(s) - chemostat , mathematics , floquet theory , stability theory , control theory (sociology) , differential equation , stability (learning theory) , substrate (aquarium) , control (management) , mathematical analysis , computer science , ecology , physics , biology , quantum mechanics , nonlinear system , machine learning , genetics , artificial intelligence , bacteria
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.