Modelling nitrogen dynamics of a constructed wetland: Nutrient removal process with variable yield

In this paper, a new mathematical modeling of rhizosphere microbial degradation with impulsive diffusion is proposed. By using the Floquet theorem, we find the rhizosphere microbe-eradication periodic solution is globally asymptotically stable if some conditions are satisfied. At the same time we also obtain the permanent conditions of the nutrients and rhizosphere microbe. Finally, a system of equations is solved by using a numerical simulation to justify our results. MSC: 34C05; 92D25

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“…Author details 1 Department of Mathematics, Huanghuai University, Zhumadian, Henan 463000, P.R. China.…”

Section: Discussionmentioning

confidence: 99%

Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient

Zhao

Song²,

Pang

2016

Adv Differ Equ

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“…B. Burgin (2000), W. M. Getz & J. O. Lloyd-Smith (2006), and S. R.-J. Jang (2008) were interested in discrete epidemic models while K. Bunwong et al (2009) studied nutrient removal process on a continuous time model.…”

Section: The Classical Concept Of Ecological Modellingmentioning

confidence: 99%

Numerical Simulation on Ecological Interactions in Time and Space

Bunwong¹

2011

Numerical Analysis - Theory and Application

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“…The removal of the sewage from a water body by the biodegradation has been investigated by many researchers [3][4][5][6][7][8][9][10][11][12][13][14][15]. In [14], pollutant removal process of a constructed wetland is simulated by the following model:…”

Section: Introductionmentioning

confidence: 99%

“…The meaning of other parameters is also given in [14]. Scott et al [15] propose a mathematical model for dispersal of bacterial inoculants colonizing the water rhizosphere to describe bacterial growth and movement in the rhizosphere.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Pang

Zhao

et al. 2015

Discrete Dynamics in Nature and Society

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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.

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Modelling nitrogen dynamics of a constructed wetland: Nutrient removal process with variable yield

Cited by 6 publications

References 14 publications

Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient

Mathematical modeling of rhizosphere microbial degradation with impulsive diffusion on nutrient

Numerical Simulation on Ecological Interactions in Time and Space

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

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