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Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control

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  • Fengmei Tao
  • Zhong Zhao
  • Lansun Chen

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.

Suggested Citation

  • Fengmei Tao & Zhong Zhao & Lansun Chen, 2018. "Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-10, October.
    • Handle: RePEc:hin:jnddns:6401059
    DOI: 10.1155/2018/6401059
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    Cited by:

    1. Li, Wenjie & Ji, Jinchen & Huang, Lihong & Zhang, Ying, 2023. "Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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