A competition model in the chemostat with allelopathy and substrate inhibition

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چکیده

<p style='text-indent:20px;'>A model of two microbial species in a chemostat competing for single resource is considered, where one the competitors that produces toxin, which lethal to other competitor (allelopathic inhibition), itself inhibited by substrate. Using general growth rate functions species, necessary and sufficient conditions existence local stability all equilibria four-dimensional system are determined according operating parameters represented dilution input concentration With Michaelis-Menten or Monod functions, it well known can have unique positive equilibrium unstable as long exists. If non monotonic considered (which case when there substrate shown new point exists be stable system. We describe its diagram, bifurcation diagram giving behavior with respect parameters. By means this we show presents set fifteen possible behaviors: washout, competitive exclusion coexistence, multi-stability, occurrence limit cycles through super-critical Hopf bifurcations, homoclinic bifurcations flip bifurcation. This very useful understand from both mathematical biological points view.</p>

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ژورنال

عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B

سال: 2022

ISSN: ['1531-3492', '1553-524X']

DOI: https://doi.org/10.3934/dcdsb.2021120