ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Dynamics Of Non-stationary Macroeconomic Model


G. S. Osipenko

Sevastopol Institute of Banking,


The dynamics of a macroeconomic system in which national income, cost of money and price-level are in close interaction is studied. Such an interaction is simulated with the help of a discrete dynamic system in 3-dimensional euclidean space. The system has a curve formed by fixed points which describe a balanced state of money, goods and service markets. It has been shown that there is a foliation which is transversal to the curve, each layer being invariant for the system. There are layers where balanced state can be both stable and unstable. The system dynamics is changing from layer to layer. There are two routes of bifurcations. The first one runs on the following scheme: a fixed point looses its stability resulting in appearance of a stable invariant ellipse (Neimark-Sacker bifurcations). In the ellipse periodic hyperbolic orbits appear and cause chaos through transversal intersection of stable and unstable manifolds. The other way leads to chaos through the period doubling bifurcation. Minor random perturbations of the system have been viewed. In this case the system does not preserve fixed points and the invariance of layers, which leads to more complicated dynamics.

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