An interaction model for livestock farming and steppe ecosystem

This work builds a macro model for livestock farming based on aggregation of initial micro description for rational control of total number of vintage livestock (age cohorts). Solution of an optimal problem for cohort total number of livestock gives the age limit for animals, the volume of the credits for the farm, the speed of slaughter, and the conditions on purchase of young animals. The integral equation for the equilibrium price of young animals is obtained. A steppe ecosystem model based on carbon cycle is constructed. The model takes into account some external influences. It is taken into account that the maintenance of animals damages the nature. Numerical experiments on the obtained ecological–economic model with the rational expectations are done by high performance computing on MVS 1000M at Joint Supercomputing Center (Moscow). On the basis of a base scenario the developments of processes in several alternatives are built and calculated. One scenario demonstrates a regime in which the area of natural pastures is reduced by the virtue of external human activity.