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Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake

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  • Fu, Guifang
  • Ma, Wanbiao

Abstract

In this paper, we consider a simple chemostat model involving a single species feeding on redundant substrate with a variable yield term. Many experiments indicate that very high substrate concentrations actually inhibit growth. Instead of assuming the prevalent Monod kinetics for growth rate of cells, we use a non-monotonic functional response function to describe the inhibitory effect. The existence of periodic solutions when certain parameters of the model assuming a specific ratio is shown.

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  • Fu, Guifang & Ma, Wanbiao, 2006. "Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 845-850.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:4:p:845-850
    DOI: 10.1016/j.chaos.2005.05.056
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    Cited by:

    1. Yan, Rong & Sun, Shulin, 2020. "Stochastic characteristics of a chemostat model with variable yield," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Mu, Yu & Li, Zuxiong, 2023. "Bifurcation dynamics of a delayed chemostat system with spatial diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 186-204.
    3. Jiao, Jianjun & Yang, Xiaosong & Chen, Lansun & Cai, Shaohong, 2009. "Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2280-2287.

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