The Dynamical Model of Herd Turnover of Dairy Cattle
The paper deals with the herd turnover of dairy cattle. A dynamical model for the herd turnover is constructed on the basis of the exact solution of a system of recurrent equations connecting the main age categories of the herd. It is shown that the solution of the task comes to the solving difference equations of the third order. The exact solutions of these equations have been found under the assumption that the reproduction rates of the herd are permanent. On the basis of these solutions one can predict the livestock number of the main age groups of the herd at any production time horizon. It is shown that the decisive factor in the herd turnover is the culling coefficient. The model makes it possible to quickly calculate the livestock number with varying values of the determining coefficients. The results of the study can be applied for forecasting the possibilities of dairy herd development, optimization and adjustment to livestock number, taking into account the basic reproduction indicators in the field.