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Existence of periodic solutions of a continuous flow bioreactor model with impulsive control in microorganisms

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Abstract

In this paper, we aim to investigate the dynamics and existence of periodic solutions of a state-dependent impulsive model for continuous flow bioreactors. In this model, the Monod’s growth rate is employed and an impulsive control strategy is used to control the quantity of microorganisms. Our study shows all solutions of the model are bounded; and the order-1 periodic solution exists under certain conditions. At the end of this paper, numerical simulations have been carried out to demonstrate our theoretical results and the performance of the bioreactor.

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Authors and Affiliations

  1. Department of Mathematics, Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Zhenzhen Chen & Tonghua Zhang

  2. Department of Chemical Engineering, Curtin University of Technology, Perth, WA, 6845, Australia

    Moses O. Tadé

  3. School of Engineering, Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Geoffrey Brooks

Authors
  1. Zhenzhen Chen
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  2. Tonghua Zhang
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  3. Moses O. Tadé
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  4. Geoffrey Brooks
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Correspondence to Tonghua Zhang.

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Chen, Z., Zhang, T., Tadé, M.O. et al. Existence of periodic solutions of a continuous flow bioreactor model with impulsive control in microorganisms. J. Appl. Math. Comput. 53, 471–486 (2017). https://doi.org/10.1007/s12190-015-0977-4

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  • DOI: https://doi.org/10.1007/s12190-015-0977-4

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