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...
Main Authors: | , , , |
---|---|
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 |
id |
doaj-4dbf522d63924f23b2f479ec4c497498 |
---|---|
record_format |
Article |
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 |
work_keys_str_mv |
AT zhongzhao impulsivestatefeedbackcontroloftherhizospheremicrobialdegradationinthewetlandplant AT liuyongpang impulsivestatefeedbackcontroloftherhizospheremicrobialdegradationinthewetlandplant AT zhanpingzhao impulsivestatefeedbackcontroloftherhizospheremicrobialdegradationinthewetlandplant AT chengguangluo impulsivestatefeedbackcontroloftherhizospheremicrobialdegradationinthewetlandplant |
_version_ |
1725756107655217152 |