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A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input

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  • Xiang, Zhongyi
  • Song, Xinyu

Abstract

In this paper, we present and analyze a simple model for a chemostat with plasmid-bearing and plasmid-free organisms and periodically pulsed substrate. We obtain an exact periodic solution with positive concentrations of substrate and plasmid-free organism, and furthermore, we prove that the periodic solution is stable if the impulsive period is more than some critical value and meanwhile we prove that system is permanent if the impulsive period is less than some critical value. Finally, we give a brief discussion and find that periodically pulsed input destroys the equilibria of the unforced continuous system.

Suggested Citation

  • Xiang, Zhongyi & Song, Xinyu, 2007. "A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1419-1428.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1419-1428
    DOI: 10.1016/j.chaos.2005.11.069
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    References listed on IDEAS

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    1. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
    2. Zhang, Yujuan & Xiu, Zhilong & Chen, Lansun, 2005. "Chaos in a food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 159-166.
    3. El-Sheikh, M.M.A. & Mahrouf, S.A.A., 2005. "Stability and bifurcation of a simple food chain in a chemostat with removal rates," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1475-1489.
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    1. López-Ruiz, Ricardo & Fournier-Prunaret, Danièle, 2009. "Periodic and chaotic events in a discrete model of logistic type for the competitive interaction of two species," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 334-347.

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