CONSTRUCTION OF SOLUTIONS WITH THE GIVEN LIMIT PROPERTIES FOR THE SYSTEMS DESCRIBING THE CHEMOSTAT MODELS
Abstract
A system of three differential equations describing the process of continuous bacteria cultivation in a chemostat is considered. For a simple food chain described by the dynamic Michaelis-Menten chemostat model a two-parameter analytical solution is obtained. An algorithm and software allowing one to find an explicit form of solutions with the given limit properties have been constructed with the usage of the CAS Mathematica capabilities. Examples, in which it is possible to model the survival or extinction of one or two microorganisms and to find initial concentration ranges, provide “competitive exclusion” or coexistence of the both organisms, are given.
About the Authors
A. V. Chichurin
A.S. Pushkin Brest State University
Belarus
Belarus
A. N. Shvychkina
A.S. Pushkin Brest State University
Belarus
Belarus
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