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Impulsive control of a continuous-culture and flocculation harvest chemostat model

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  • Tongqian Zhang
  • Wanbiao Ma
  • Xinzhu Meng

Abstract

In this paper, a new mathematical model describing the process of continuous culture and harvest of microalgaes is proposed. By inputting medium and flocculant at two different fixed moments periodically, continuous culture and harvest of microalgaes is implemented. The mathematical analysis is conducted and the whole dynamics of model is investigated by using theory of impulsive differential equations. We find that the model has a microalgaes-extinction periodic solution and it is globally asymptotically stable when some certain threshold value is less than the unit. And the model is permanent when some certain threshold value is larger than the unit. Then, according to the threshold, the control strategies of continuous culture and harvest of microalgaes are discussed. The results show that continuous culture and harvest of microalgaes can be archived by adjusting suitable input time, input amount of medium or flocculant. Finally, some numerical simulations are carried out to verify the control strategy.

Suggested Citation

  • Tongqian Zhang & Wanbiao Ma & Xinzhu Meng, 2017. "Impulsive control of a continuous-culture and flocculation harvest chemostat model," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(16), pages 3459-3469, December.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:16:p:3459-3469
    DOI: 10.1080/00207721.2017.1384861
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    2. 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.
    3. Leung, Dennis Y.C. & Wu, Xuan & Leung, M.K.H., 2010. "A review on biodiesel production using catalyzed transesterification," Applied Energy, Elsevier, vol. 87(4), pages 1083-1095, April.
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    1. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.

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