The invariance principle of La-Salle and mathematical models for the evolution of microbial populations

• Main Authors: Yu. M. Aponin, E. A. Aponina
• Format: Article
• Language: Russian
• Published: Institute of Computer Science 2011-06-01
• Series: Компьютерные исследования и моделирование
• Subjects: evolution of microbial populations; mathematical modeling; Liapunov’s function; bounded globally attracting set
• Online Access: http://crm.ics.org.ru/uploads/crmissues/crm_2011_2/11207.pdf

A mathematical model for the evolution of microbial populations during prolonged cultivation in a chemostat has been constructed. This model generalizes the sequence of the well-known mathematical models of the evolution, in which such factors of the genetic variability were taken into account as chromosomal mutations, mutations in plasmid genes, the horizontal gene transfer, the plasmid loss due to cellular division and others. Liapunovs function for the generic model of evolution is constructed. The existence proof of bounded, positive invariant and globally attracting set in the state space of the generic mathematical model for the evolution is presented because of the application of La-Salles theorem. The analytic description of this set is given. Numerical methods for estimate of the number of limit sets, its location and following investigation in the mathematical models for evolution are discussed.