Abstract
In this paper, we propose a chemostat model of competition between plasmid-bearing and plasmid-free organism with the impulsive state feedback control. The sufficient condition for existence of the positive period-1 solution is obtained by means of successor function and the qualitative properties of the corresponding continuous system. We show that the impulsive control system is more effective than the corresponding continuous system if we choose a suitable threshold value of the state feedback control in the process of manufacturing the desired products through genetically modified techniques. Furthermore, a new method of proving the stability of the order-1 periodic solution is given based on the theory of the limit cycle of the continuous dynamical system. Finally, mathematical results are justified by some numerical simulations.
Highlights
With the rapid development of biotechnology, manufacturing the desired products through genetically modified techniques has been widely applied in many fields, such as agriculture, industrial biotechnology, and medicine
We propose a chemostat model of competition between plasmid-bearing and plasmid-free organism with the impulsive state feedback control
The plasmid is lost in the reproductive process, which will bring some negative effects on the desired products
Summary
With the rapid development of biotechnology, manufacturing the desired products through genetically modified techniques has been widely applied in many fields, such as agriculture, industrial biotechnology, and medicine. Yuan et al [6] proposed a model for competition between plasmid-bearing and plasmid-free organisms in the chemostat with an external inhibitor and obtained some sufficient conditions of global attractivity to the extinction equilibria by constructing appropriate Lyapunov-like functionals. As far as the authors know, little information is given about the introduction of the impulsive state feedback control into chemostat model of competition between plasmid-bearing and plasmid-free organism. We will formulate a mathematical model of competition between plasmid-bearing and plasmid-free organism with the impulsive state feedback control so as to further improve the efficiency of the desired products in the process of the genetic alteration. We give some numerical simulations and a brief discussion
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