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Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant

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  • Zhong Zhao
  • Liuyong Pang
  • Zhanping Zhao
  • Chengguang Luo

Abstract

The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.

Suggested Citation

  • Zhong Zhao & Liuyong Pang & Zhanping Zhao & Chengguang Luo, 2015. "Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, May.
    • Handle: RePEc:hin:jnddns:612354
    DOI: 10.1155/2015/612354
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