Journal of Mathematical Chemistry

, Volume 47, Issue 4, pp 1224–1239 | Cite as

Impulsive state feedback control of the microorganism culture in a turbidostat

  • Zhong Zhao
  • Li Yang
  • Lansun Chen
Original Paper


In this paper, a mathematical model with the impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of order-1 and order-2 periodic solutions are obtained by the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state and the initial concentration of microorganism and substrate. Finally, some discussions and numerical simulations are given.


Turbidostat Impulsive state feedback control Period-1 solution Period-2 solution 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsHuanghuai UniversityZhumadianPeople’s Republic of China
  2. 2.Department of Applied MathematicsDalian University of TechnologyDalianPeople’s Republic of China

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