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Mathematical model for diffusion of the rhizosphere microbial degradation with impulsive feedback control
- Source :
- Journal of Biological Dynamics, Vol 14, Iss 1, Pp 566-577 (2020)
- Publication Year :
- 2020
- Publisher :
- Informa UK Limited, 2020.
-
Abstract
- 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.
- Subjects :
- Time Factors
Feedback control
Models, Biological
01 natural sciences
Stability (probability)
Feedback
Limit cycle
order-1 periodic solution
0101 mathematics
Diffusion (business)
rhizosphere diffusion
lcsh:QH301-705.5
lcsh:Environmental sciences
Ecology, Evolution, Behavior and Systematics
square approximation
Mathematics
lcsh:GE1-350
Rhizosphere
Bacteria
Ecology
010102 general mathematics
rhizosphere model
010101 applied mathematics
lcsh:Biology (General)
Control system
Biological system
Subjects
Details
- ISSN :
- 17513766 and 17513758
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- Journal of Biological Dynamics
- Accession number :
- edsair.doi.dedup.....7483e34149f262798b6783a293e5164f