Piecewise chemostat model with control strategy

Jin Yang and Guangyao Tang

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 156, issue C, 126-142

Abstract: The chemostat model involving control strategy is either on or off which can be defined by piecewise (or non-smooth) dynamic system. With the aim of controlling the concentration of microorganism within a reasonable range, piecewise chemostat models concerning control strategy with two thresholds are established and investigated. For the chemostat models with a single threshold, all types of equilibria are addressed. Then local bifurcations with respect to boundary node bifurcations are studied by utilizing theoretical and numerical methods. Furthermore, global bifurcations involving touching bifurcation of the sliding cycle, buckling bifurcation of the sliding cycle and sliding crossing bifurcation are discussed. For the chemostat models with two thresholds, No control state and Control state switches are needed to maintain periodic oscillations for microorganism population. Besides, the effects of width of threshold window on the durations or number of Control state and No control state switches are discussed, if the threshold window becomes too large or small, then periodical fluctuation cannot be maintained. Moreover, under certain conditions the microorganism concentration always fluctuates periodically no matter how the threshold window changes. All results indicate that the microorganism concentration can either fluctuate periodically or stabilize at different constants. Therefore, the threshold windows should be chosen carefully according to different aims of control.

Keywords: Piecewise; Threshold window; Periodic solution; Bifurcations; Duration (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:156:y:2019:i:c:p:126-142

DOI: 10.1016/j.matcom.2018.07.004

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