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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Published in | Journal of biological dynamics Vol. 14; no. 1; pp. 566 - 577 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Abingdon
Taylor & Francis
01.01.2020
Taylor & Francis Ltd Taylor & Francis Group |
Subjects | |
Online Access | Get full text |
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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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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1751-3758 1751-3766 |
DOI: | 10.1080/17513758.2020.1786860 |