Deterministic models and identification of their parameters

Abstract

This article deals with a possibility to identify parameters of a selected growth model of
two populations coupled by a predator–prey interaction from a set of observed data. It
starts with a brief description of the the Gause-type model and of a property (interior
equilibrium stability) important from a point of view of an application. Subsequently,
data for four forms of the trophic function are simulated and then, a noise was added
to the simulated data such that the coefficients of variation equal to 0.2, 0.3 and 0.4.
For each data set, the parameters are estimated using a procedure implemented in the
R-language package and the coordinates of equilibrium are computed. Then we can
evaluate the effect of changing variation to the values of parameters and (un)stability of
the equilibrium.