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Dynamic Complexities Of A Chemostat Model With Pulsed Input And Washout At Different Times

Author

Listed:
  • SHUWEN ZHANG

    (College of Sciences, Jimei University, Xiamen, Fujian, 361021, P. R. China)

  • DEJUN TAN

    (College of Sciences, Jimei University, Xiamen, Fujian, 361021, P. R. China)

  • HONGSHENG GU

    (Department of Mathematics, Anshan Normal University, Anshan, Liaoning, 114005, P. R. China)

Abstract

In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and periodic input and washout at different fixed times. We obtain an exact periodic solution with substrate and prey. The stability analysis for this periodic solutions yields an invasion threshold for the period of pulses of the predator. When the impulsive period is more than the threshold, there are periodic oscillations in the substrate, prey, and predator. If the impulsive period further increases, the system undergoes a complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcation, which are period-doubling and period-halving.

Suggested Citation

  • Shuwen Zhang & Dejun Tan & Hongsheng Gu, 2008. "Dynamic Complexities Of A Chemostat Model With Pulsed Input And Washout At Different Times," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 65-76.
    • Handle: RePEc:wsi:acsxxx:v:11:y:2008:i:01:n:s0219525908001490
    DOI: 10.1142/S0219525908001490
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    References listed on IDEAS

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    1. K.-H. Waldmann, 1985. "On Bounds for Dynamic Programs," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 220-232, May.
    2. Unknown, 1985. "Abstracts Of Selected Papers," Northeastern Journal of Agricultural and Resource Economics, Northeastern Agricultural and Resource Economics Association, vol. 14(2), pages 1-3, October.
    3. N/A, 1985. "Obituary—Alan Richmond Prest," Environment and Planning C, , vol. 3(1), pages 1-1, March.
    4. N/A, 1985. "Public Services Pay in the 1980s," National Institute Economic Review, National Institute of Economic and Social Research, vol. 112(1), pages 31-34, May.
    5. anonymous, 1985. "Reserve Bank annual report," Reserve Bank of New Zealand Bulletin, Reserve Bank of New Zealand, vol. 48, august.
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