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Piecewise chemostat model with control strategy

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  • Yang, Jin
  • Tang, Guangyao

Abstract

The chemostat model involving control strategy is either on or off which can be defined by piecewise (or non-smooth) dynamic system. With the aim of controlling the concentration of microorganism within a reasonable range, piecewise chemostat models concerning control strategy with two thresholds are established and investigated. For the chemostat models with a single threshold, all types of equilibria are addressed. Then local bifurcations with respect to boundary node bifurcations are studied by utilizing theoretical and numerical methods. Furthermore, global bifurcations involving touching bifurcation of the sliding cycle, buckling bifurcation of the sliding cycle and sliding crossing bifurcation are discussed. For the chemostat models with two thresholds, No control state and Control state switches are needed to maintain periodic oscillations for microorganism population. Besides, the effects of width of threshold window on the durations or number of Control state and No control state switches are discussed, if the threshold window becomes too large or small, then periodical fluctuation cannot be maintained. Moreover, under certain conditions the microorganism concentration always fluctuates periodically no matter how the threshold window changes. All results indicate that the microorganism concentration can either fluctuate periodically or stabilize at different constants. Therefore, the threshold windows should be chosen carefully according to different aims of control.

Suggested Citation

  • Yang, Jin & Tang, Guangyao, 2019. "Piecewise chemostat model with control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 126-142.
    • Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:126-142
    DOI: 10.1016/j.matcom.2018.07.004
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    References listed on IDEAS

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    1. Yang, Jin & Tang, Guangyao & Tang, Sanyi, 2017. "Modelling the regulatory system of a chemostat model with a threshold window," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 220-235.
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    3. Gakkhar, Sunita & Sahani, Saroj Kumar, 2009. "A model for delayed effect of toxicant on resource-biomass system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 912-922.
    4. Yuan Tian & Kaibiao Sun & Andrzej Kasperski & Lansun Chen, 2010. "Nonlinear Modelling and Qualitative Analysis of a Real Chemostat with Pulse Feeding," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-18, September.
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    2. Li, Wenjie & Ji, Jinchen & Huang, Lihong & Zhang, Ying, 2023. "Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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