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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 612354, 7 pages
http://dx.doi.org/10.1155/2015/612354
Research Article

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

Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, China

Received 13 October 2014; Revised 23 February 2015; Accepted 23 February 2015

Academic Editor: Carlo Piccardi

Copyright © 2015 Zhong Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.