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Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate

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  • Wang, Fengyan
  • Pang, Guoping
  • Lu, Zhengyi

Abstract

A model of a Beddington–DeAngelis type food chain chemostat with periodically varying dilution rate is considered. The system consists of one predator, one prey and limiting substrate. The periodic solutions of the subsystem with substrate and prey, which are the boundary periodic solutions of the system, are obtained. The stability analysis of the boundary periodic solution yields a predator invasion threshold. Above this threshold, there are periodic oscillations in the system. Furthermore, a model with sinusoidal dilution rate is numerically simulated. By bifurcation diagrams with different bifurcation parameters, the periodic system shows two kinds of bifurcations, whose are period-doubling and period-halving.

Suggested Citation

  • Wang, Fengyan & Pang, Guoping & Lu, Zhengyi, 2009. "Analysis of a Beddington–DeAngelis food chain chemostat with periodically varying dilution rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1609-1615.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1609-1615
    DOI: 10.1016/j.chaos.2007.09.041
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    References listed on IDEAS

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    1. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 826-839.
    2. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2008. "Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 731-742.
    3. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Monod–Haldene type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 181-194.
    4. Wang, Fengyan & Hao, Chunping & Chen, Lansun, 2007. "Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1547-1561.
    5. Wang, Fengyan & Zhang, Shuwen & Chen, Lansun & Sun, Lihua, 2006. "Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 447-458.
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    Cited by:

    1. Wang, Fengyan & Pang, Guoping & Zhang, Shuwen, 2009. "Analysis of a Lotka–Volterra food chain chemostat with converting time delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2786-2795.
    2. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.

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