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

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 feed...

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Main Authors: Zhong Zhao, Liuyong Pang, Zhanping Zhao, Chengguang Luo
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/612354
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spelling doaj-4dbf522d63924f23b2f479ec4c4974982020-11-24T22:25:49ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/612354612354Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland PlantZhong Zhao0Liuyong Pang1Zhanping Zhao2Chengguang Luo3Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, ChinaDepartment of Mathematics, Huanghuai University, Zhumadian, Henan 463000, ChinaDepartment of Mathematics, Huanghuai University, Zhumadian, Henan 463000, ChinaDepartment of Mathematics, Huanghuai University, Zhumadian, Henan 463000, ChinaThe 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.http://dx.doi.org/10.1155/2015/612354
collection DOAJ
language English
format Article
sources DOAJ
author Zhong Zhao
Liuyong Pang
Zhanping Zhao
Chengguang Luo
spellingShingle Zhong Zhao
Liuyong Pang
Zhanping Zhao
Chengguang Luo
Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
Discrete Dynamics in Nature and Society
author_facet Zhong Zhao
Liuyong Pang
Zhanping Zhao
Chengguang Luo
author_sort Zhong Zhao
title Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
title_short Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
title_full Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
title_fullStr Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
title_full_unstemmed Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant
title_sort impulsive state feedback control of the rhizosphere microbial degradation in the wetland plant
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/612354
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AT zhanpingzhao impulsivestatefeedbackcontroloftherhizospheremicrobialdegradationinthewetlandplant
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