TY - JOUR

T1 - Developing industries in cooperative interaction

T2 - Equilibrium and stability in processes with lag

AU - Kirjanen, A. I.

AU - Malafeyev, O. A.

AU - Redinskikh, N. D.

PY - 2017

Y1 - 2017

N2 - A mathematical model of dynamic interaction between mining and processing industries is formalized and studied in the paper. The process of interaction is described by a system of two delay differential equations. The criterion for asymptotic stability of nontrivial equilibrium point is obtained when both industries co-work steadily. The problem is reduced to finding stability criterion for quasi-polynomial of second order. Time intervals between deliveries of raw materials which make it possible to preserve stable interaction between the two industries are found.

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

KW - Coefficient criteria for asymptotic stability

KW - Delay

KW - Differential equations

KW - Dynamic cooperative interaction

KW - Mining and processing industries

UR - http://www.scopus.com/inward/record.url?scp=85035805326&partnerID=8YFLogxK

U2 - 10.19139/soic.v5i4.357

DO - 10.19139/soic.v5i4.357

M3 - Article

AN - SCOPUS:85035805326

VL - 5

SP - 341

EP - 347

JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

SN - 2311-004X

IS - 4

ER -