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Chaos in a food chain chemostat with pulsed input and washout

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  • Zhang, Yujuan
  • Xiu, Zhilong
  • Chen, Lansun

Abstract

A food-chain chemostat with periodically pulsed input and washout is presented and analyzed. We prove that when the period of pulses is equal to some critical value, there exists a transcritical bifurcation. When the period is more than the critical value, the zooplankton-free periodic solution loses stability, and nutrient, phytoplankton and zooplankton coexist on a periodic solution of period T. If the period is further increase, the system undergoes a series of period-doubling bifurcations leading to chaos. Moreover, the system is also characterized by non-unique dynamic. Finally, we give a brief discussion and find that periodically pulsed input and washout destroys the equilibria of the unforced continuous system and initiates chaos.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:1:p:159-166
    DOI: 10.1016/j.chaos.2004.12.040
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    2. Toth, Damon J.A., 2008. "Strong resonance and chaos in a single-species chemostat model with periodic pulsing of resource," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 55-69.
    3. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    4. 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.
    5. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2007. "The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1772-1785.
    6. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
    7. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
    8. Wijeratne, A.W. & Yi, Fengqi & Wei, Junjie, 2009. "Bifurcation analysis in the diffusive Lotka–Volterra system: An application to market economy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 902-911.

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