Evolutionary age-structured cell dynamic models for plant systems

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Vitalii Akimenko, Yurii Zahorodnii

Taras Shevchenko National University of Kyiv, Ukraine

We have analyzed the evolution of the cells aggregation in the frame of polycyclic age-structured model using both the analytical technique and numerical simulation approaches. In the first case we have reduced the temporal-age initial boundary problem for the transport equation to the Volterra integral equation and have resolved it used infinite convergent series. In the second one we have built explicit two layers numerical differential scheme with second order of approximation by time and first order approximation by age with explicit recurrent formulas for boundary condition. We considered the set of income equation coefficients as a set of parametrized algebraic functions with compact sets of parameter definition. The parameters estimation problem was resolved for the both approaches for the observed within 3 seasons time series data of overground dried mass of hop plant. As the relative errors of deviation of simulated curves from the points of observed data were less than 7%, we have concluded that polycyclic age-structured models of cell aggregation are enough efficient to describe the temporal evolution of plant cells mass.