2017/06/21 by Dimitrios Voulgarelis, Voulgarelis, Dimitrios, Ajoy Valayudhan +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #34E05 #34F05 #35Q84 #60H10 #92B05 #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1706.07078
openalex publication_date 2017/06/21 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
This paper formulates two 3D stochastic differential equations (SDEs) of two\nmicrobial populations in a chemostat competing over a single substrate. The two\nmodels have two distinct noise sources. One is general noise whereas the other\nis dilution rate induced noise. Nonlinear Monod growth rates are assumed and\nthe paper is mainly focused on the parameter values where coexistence is\npresent deterministically. Nondimensionalising the equations around the point\nof intersection of the two growth rates leads to a large parameter which is the\nnondimensional substrate feed. This in turn is used to perform an asymptotic\nanalysis leading to a reduced 2D system of equations describing the dynamics of\nthe populations on and close to a line of steady states retrieved from the\ndeterministic stability analysis. That reduced system allows the formulation of\na spatially 2D Fokker-Planck equation which when solved numerically admits\nresults similar to those from simulation of the SDEs. Contrary to previous\nsuggestions, one particular population becomes dominant at large times.\nFinally, we brie y explore the case where death rates are added.\n