Mathematical model for diffusion of the rhizosphere microbial degradation with impulsive feedback control

Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizo...

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Bibliographic Details
Published inJournal of biological dynamics Vol. 14; no. 1; pp. 566 - 577
Main Authors Zhao, Zhong, Chen, Ying, Li, Qiuying, Wu, Xianbin
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.01.2020
Taylor & Francis Ltd
Taylor & Francis Group
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Summary:Considering the rhizosphere microbes easily affected by the environmental factors, we formulate a three-dimensional diffusion model of the rhizosphere microbes with the impulsive feedback control to describe the complex degradation and movement by introducing beneficial microbes into the plant rhizosphere. The sufficient conditions for existence of the order-1 periodic solution are obtained by using the geometrical theory of the impulsive semi-dynamical system. We show the impulsive control system tends to an order-1 periodic solution if the control measures are achieved. Furthermore, we investigate the stability of the order-1 periodic solution by means of a novel method introduced in the literature [Y. Ye, The Theory of the Limit Cycle, Shanghai Science and Technology Press, 1984.]. Finally, mathematical results are justified by some numerical simulations.
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ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2020.1786860