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Study of chaotic behavior in predator–prey interactions in a chemostat

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  • Ali, Emad
  • Asif, Mohammed
  • Ajbar, AbdelHamid

Abstract

This paper investigates the complex dynamics resulting from interactions between one predator and one prey in a chemostat. A standard model is extended by allowing the yield coefficient associated with the prey to vary linearly with the substrate concentration. When this dependence is negligible, the proposed model is reduced to the classical constant yield model which was shown in the literature to produce periodic behavior for a wide range of parameters. In this paper we analyze the proposed model and we show that while the static behavior is relatively simple, the dynamics are complex and involve limit cycles and period doubling sequences leading to chaos. Numerical simulations are also presented to analyze the model equations and to determine the effect of its parameters on the resulting dynamics. The proposed model could serve as a basis to re-examine the importance of variable yield coefficients in predicting complex behavior in predator–prey interactions in the chemostat.

Suggested Citation

  • Ali, Emad & Asif, Mohammed & Ajbar, AbdelHamid, 2013. "Study of chaotic behavior in predator–prey interactions in a chemostat," Ecological Modelling, Elsevier, vol. 259(C), pages 10-15.
    • Handle: RePEc:eee:ecomod:v:259:y:2013:i:c:p:10-15
    DOI: 10.1016/j.ecolmodel.2013.02.029
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    References listed on IDEAS

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    1. Zhao, Min & Lv, Songjuan, 2009. "Chaos in a three-species food chain model with a Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2305-2316.
    2. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a three species food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1469-1480.
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    Cited by:

    1. 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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