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A mathematical model of dynamic interaction between mining and processingindustries is formalized and studied in the paper. The process of interactionis described by a system of two delay differential equations. The criterion forasymptotic stability of nontrivial equilibrium point is obtained when bothindustries co-work steadily. The problem is reduced to finding stabilitycriterion for quasi-polynomial of second order. Time intervals betweendeliveries of raw materials which make it possible to preserve stableinteraction between the two industries are found.

Stability in the process with lag of interaction between mining and processing industries