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Dynamic analysis of lactic acid fermentation with impulsive input

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Abstract

In this paper, a mathematical model for the lactic acid fermentation in membrane bioreactor is investigated. Using the Floquet’s theorem and small amplitude perturbation method, we obtain the biomass-free periodic solution is locally stable if some conditions are satisfied. The permanent conditions of the system are also given. Furthermore, in a certain limiting case it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations.

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Authors and Affiliations

  1. Department of Mathematics, Huanghuai University, Zhumadian, 463000, Henan, People’s Republic of China

    Zhong Zhao

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

    Zhong Zhao & Lansun Chen

Authors
  1. Zhong Zhao
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  2. Lansun Chen
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Correspondence to Zhong Zhao.

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Zhao, Z., Chen, L. Dynamic analysis of lactic acid fermentation with impulsive input. J Math Chem 47, 1189–1208 (2010). https://doi.org/10.1007/s10910-008-9494-0

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  • DOI: https://doi.org/10.1007/s10910-008-9494-0

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