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Periodic solution of a turbidostat model with impulsive state feedback control

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Abstract

In this paper, a turbidostat model with impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control may have order one periodic solution, and the sufficient condition for existence and stability of order one periodic solution is gotten as well. For some special cases, it is shown that in the system an order two periodic solution may exist. Our results show that the control measure is effective and reliable.

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Authors and Affiliations

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

    Zuxiong Li & Lansun Chen

  2. Jishou University, Jishou, 416000, People’s Republic of China

    Zuxiong Li

Authors
  1. Zuxiong Li
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  2. Lansun Chen
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Correspondence to Zuxiong Li.

Additional information

Supported by National Natural Science Foundation of China (No: 10771179).

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Li, Z., Chen, L. Periodic solution of a turbidostat model with impulsive state feedback control. Nonlinear Dyn 58, 525–538 (2009). https://doi.org/10.1007/s11071-009-9498-8

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  • DOI: https://doi.org/10.1007/s11071-009-9498-8

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