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Discrete Dynamics in Nature and Society Volume 2018 ,2018-10-23
Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control
Research Article
Fengmei Tao 1 Zhong Zhao 2 Lansun Chen 3
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DOI:10.1155/2018/6401059
Received 2018-06-27, accepted for publication 2018-09-16, Published 2018-09-16
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摘要

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.

授权许可

Copyright © 2018 Fengmei Tao et al. 2018
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.

图表

The existence of order-1 periodic solution of system (6) for H

The stability of the order-1 periodic solution of system (3) for x2

The stability of the order-1 periodic solution of system (3) for x2

Time series and phase portrait of the globally asymptotical stability of the positive equilibrium (x∗,y∗) with the parameters A=12,q=0.4,B=3.5.

Time series and phase portrait of the globally asymptotical stability of the positive equilibrium (x∗,y∗) with the parameters A=12,q=0.4,B=3.5.

Time series and phase portrait of the globally asymptotical stability of the positive equilibrium (x∗,y∗) with the parameters A=12,q=0.4,B=3.5.

Time series and phase portrait of the semitrivial periodic solution of system (6) with the parameters A=5, q=0.3, B=3.5, H=0.4, E1=0.3, E2=0.6.

Time series and phase portrait of the semitrivial periodic solution of system (6) with the parameters A=5, q=0.3, B=3.5, H=0.4, E1=0.3, E2=0.6.

Time series and phase portrait of the semitrivial periodic solution of system (6) with the parameters A=5, q=0.3, B=3.5, H=0.4, E1=0.3, E2=0.6.

Time series and phase portrait of the order-1 periodic solution of system (6) with the parameters A=12,q=0.4,B=3.5, H=0.3748366014, E1=0.01,E2=0.6.

Time series and phase portrait of the order-1 periodic solution of system (6) with the parameters A=12,q=0.4,B=3.5, H=0.3748366014, E1=0.01,E2=0.6.

Time series and phase portrait of the order-1 periodic solution of system (6) with the parameters A=12,q=0.4,B=3.5, H=0.3748366014, E1=0.01,E2=0.6.

通讯作者

Zhong Zhao.Department of Mathematics, Huanghuai University, Zhumadian 463000, Henan, China, huanghuai.edu.cn.zhaozhong8899@163.com

推荐引用方式

Fengmei Tao,Zhong Zhao,Lansun Chen. Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control. Discrete Dynamics in Nature and Society ,Vol.2018(2018)

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