Dynamics of competitive interaction between two mining enterprises and one processing: existence and stability of the equilibrium point

Abstract

A mathematical model of dynamic interaction between two mining enterprises and one processing is formalized and studied in the paper. The process of interaction is described by a system of three delay differential equations. The criterion for asymptotic stability of nontrivial equilibrium point is obtained when all three enterprises co-work steadily. The problem is reduced to finding stability criterion for quasi-polynomial of third order. We found time intervals between deliveries of raw materials and manufacturing of finished products, in which the process of interaction of the three agents is stable.