Cycles of feasible subsystems and their application to problems in modeling historical economic dynamics

This article presents a new approach to the description of nonequilibrium historical and economic situations from the viewpoint of cycles with maximum inclusion of consistent subsystems of relevant systems of constraints, inequalities, or equations. It is noted that conditions of the existence of simple cycles in graphs of maximum consistent subsystems are bound with the generalized committee solutions of such systems. The class of the linear constraint systems of special interest includes the so-called uniformly distributed (according to Gale) systems of inequalities. The structure of graphs of maximum consistent subsystems of such systems is investigated.