Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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FEEDBACK CONTROL FOR A TURBIDOSTAT MODEL WITH RATIO-DEPENDENT GROWTH RATE

  • Hu, Xiaoyu (Department of Mathematics, Hubei University for Nationalities) ;
  • Li, Zuxiong (Department of Mathematics, Hubei University for Nationalities) ;
  • Xiang, Xingguo (Department of Mathematics, Hubei University for Nationalities)
  • Received : 2012.05.12
  • Accepted : 2012.10.29
  • Published : 2013.05.30
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Abstract

In this paper, a turbidostat model with ratio-dependent growth rate and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotically stable of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.

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References

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