Global dynamics of a delayed chemostat model with harvest by impulsive flocculant input View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-12

AUTHORS

Tongqian Zhang, Wanbiao Ma, Xinzhu Meng

ABSTRACT

A mathematical model describing continuous microbial culture and harvest in a chemostat, incorporating a control strategy and defined by impulsive differential equations, is presented and investigated. Theoretical results indicate that the model has a microbe-extinction periodic solution, which is globally attractive if the threshold R1 is less than unity, and the model is permanent if the threshold R2 is greater than unity. Further, we consider the control strategy under time delay and periodical impulsive effect. Analysis shows that continuous microbial culture and harvest process can be implemented by adjusting time delay, impulsive period or input amount of flocculant. Finally, we give an example with numerical simulations to illustrate the control strategy. More... »

PAGES

115

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-017-1163-9

DOI

http://dx.doi.org/10.1186/s13662-017-1163-9

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https://app.dimensions.ai/details/publication/pub.1084980710


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52 schema:description A mathematical model describing continuous microbial culture and harvest in a chemostat, incorporating a control strategy and defined by impulsive differential equations, is presented and investigated. Theoretical results indicate that the model has a microbe-extinction periodic solution, which is globally attractive if the threshold R1 is less than unity, and the model is permanent if the threshold R2 is greater than unity. Further, we consider the control strategy under time delay and periodical impulsive effect. Analysis shows that continuous microbial culture and harvest process can be implemented by adjusting time delay, impulsive period or input amount of flocculant. Finally, we give an example with numerical simulations to illustrate the control strategy.
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