Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Contents
Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 532.516
V.V. Akimenko, Yu.V. Zahorodnii

MODELING THE DYNAMICS OF THE AGE-STRUCTURED POLYCYCLIC BIOLOGICAL CELL POPULATION FOR THE PARAMETERIZED CLASS OF ALGEBRAIC FUNCTIONS

Abstract. We research the biological cells’ population dynamics on the basis of polycyclic age-structured model using both analytical method and numerical simulation. We reduce the initial-boundary-value problem for transport equation to the Volterra integral equation of second kind and resolve it by infinite convergent series. For the initial-boundary-value problem for transport equation, we obtain explicit two-layer numerical difference scheme with second order of approximation by time and first one by age with explicit recurrent formulas for boundary condition. We consider the set of main biological parameters of the system as a set of parametrized algebraic functions with compact domain of definition. The parameter identification problem is solved for the approximate analytical solutions for the data of dried biomass of hop plant observed within 3 seasons. As the maximum relative errors of deviation of simulated curves from the points of observed data are less than 11%, we conclude that polycyclic age-structured models of cells’ aggregation are efficient to describe the temporal evolution of plant cells biomass.

Keywords: age-structured model, population, evolutionary dynamics, transport equation, nonlocal boundary conditions, analytical solution, numerical modeling, parameter identification.



FULL TEXT

Акименко Виталий Владимирович, доктор техн. наук, профессор Киевского национального университета имени Тараса Шевченко,
e-mail: akvv@unicyb.kiev.ua.

Загородний Юрий Витальевич, кандидат техн. наук, доцент Киевского национального университета имени Тараса Шевченко,
e-mail: yuzagor@ukr.net.

© 2017 Kibernetika.org. All rights reserved.