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Dynamic analysis of mathematical model of ethanol fermentation with gas stripping

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Abstract

In this paper, a mathematical model for ethanol fermentation with gas stripping is investigated. Firstly, the model with continuous substrate input is taken. We study the existence and local stability of two equilibrium points. According to Poincare–Bendixson Theorem, the sufficient condition for the globally asymptotical stability of positive equilibrium point is obtained, which implies that we can get stable ethanol product. Secondly, we study the model with impulsive substrate input and obtain the sufficient condition for the local stability of cell-free periodic solution by using the Floquet’s theory of impulsive differential equation and small-amplitude perturbation skills. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical (subcritical) bifurcation. Finally, our results are confirmed by means of numerical simulation.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Chunjin Wei & Lansun Chen

  2. Science College, Jimei University, Xiamen, 361021, People’s Republic of China

    Chunjin Wei

Authors
  1. Chunjin Wei
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  2. Lansun Chen
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Correspondence to Chunjin Wei.

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Supported by National Natural Science Foundation of China (10771179).

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Wei, C., Chen, L. Dynamic analysis of mathematical model of ethanol fermentation with gas stripping. Nonlinear Dyn 57, 13–23 (2009). https://doi.org/10.1007/s11071-008-9415-6

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  • DOI: https://doi.org/10.1007/s11071-008-9415-6

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