Результаты поиска по 'chemostat':
Найдено статей: 2
  1. Aponin Yu.M., Aponina E.A.
    The invariance principle of La-Salle and mathematical models for the evolution of microbial populations
    Computer Research and Modeling, 2011, v. 3, no. 2, pp. 177-190

    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. Liapunov’s 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-Salle’s 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.

    Keywords: evolution of microbial populations, mathematical modeling, Liapunov’s function, bounded globally attracting set.
    Views (last year): 8. Citations: 3 (RSCI).
  2. Borisov A.V., Krasnobaeva L.A., Shapovalov A.V.
    Influence of diffusion and convection on the chemostat dynamics
    Computer Research and Modeling, 2012, v. 4, no. 1, pp. 121-129

    Population dynamics is considered in a modified chemostat model including diffusion, chemotaxis, and nonlocal competitive losses. To account for influence of the external environment on the population of the ecosystem, a random parameter is included into the model equations. Computer simulations reveal three dynamic modes depending on system parameters: the transition from initial state to a spatially homogeneous steady state, to a spatially inhomogeneous distribution of population density, and elimination of population density.

    Keywords: chemostat, diffusion, convection, population dynamics, nonlocal competitive losses.
    Views (last year): 1.

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