Козицький В.А. кандидат фізико-математичних наук, доцент, доцент кафедри математичної економіки та економетрії Львівського національного університету імені Івана Франка Берегова Г.І. кандидат фізико-математичних наук, доцент, доцент кафедри обчислювальної математики та програмування Національного університету «Львівська політехніка» Пабирівська Н.В. кандидат фізико-математичних наук, доцент, доцент кафедри вищої математики Національного університету «Львівська політехніка» SYSTEM DYNAMIC NONLINEAR MODELING OF PRICE STABILITY СИСТЕМНЕ ДИНАМІЧНЕ НЕЛІНІЧНЕ МОДЕЛЮВАННЯ ЦІНИ СТАБІЛЬНОСТІThe article investigates the dynamic properties of price indexes based on the system dynamics approach that is a simulation modeling approach to monetary policy analysis and design. It applies to dynamic problems that describe complex economic and social systems including information and material delays as well as feedback and circular causality. The simulation nonlinear model takes into account the nonlinear process of price adjustment. The simulation results showed that the behavior of price indexes could change dramatically that was driving by small change in initial conditions and parameters of system. It has been obtained that the inflation process looked often as unpredictable and chaotic system although it had underlying sources and its driving forces did not demonstrate pure randomness. The price dynamics should be considered in a system and dynamic view and it is important to estimate the direction and magnitudes of unemployment and inflation responses on positive and negative economic shocks.

Козицький В.А. кандидат фізико-математичних наук, доцент, доцент кафедри математичної економіки та економетрії, Львівського національного університету імені Івана Франка Пабирівська Н.В. кандидат фізико-математичних наук, доцент, доцент кафедри вищої математики, Національного університету «Львівська політехніка» Пабирівський В.В. кандидат фізико-математичних наук, доцент, доцент кафедри прикладної математики Національного університету «Львівська політехніка» PECULIARITIES OF BIFURCATION IN PRICE DYNAMICS ОСОБЛИВОСТІ БІФУРКАЦІЇ В ДИНАМІЦІ ЦІН ANNOTATION The article investigates the nonlinearities and bifurcation in dynamics of price index and inflation. The developed simulation models are based on nonlinear differential equations that demonstrate different patterns of their solutions. The behavior of inflation exhibits various dynamic properties that substantially depend on initial state of economic environment and the values of parameters that describe economic conditions. The results of modeling revealed the bifurcation points and showed that the dynamic of price in economy could move unpredictable and represent different direction of movement even for small change in initial conditions. Moreover, it has been obtained that several equilibrium points in weak economic system are possible, which demonstrate different convergence properties. The price dynamics showed strong peculiarities of bifurcation depending on vicinity of equilibrium level.

The article investigates the dynamics of price index that is described by nonlinear difference equations. The simulation model takes into account different initial positions of system as well as different parameters' values. The decision-making process depends on the values of exogenous factors that affect the system behavior and lead to stability or instability results. The simulation results revealed the bifurcation point and showed that the system can behave unpredictable and demonstrate chaos dynamics even with small change in initial conditions. If the initial value is greater than equilibrium point it has been obtained the attraction for the system. If the initial value is less than equilibrium point it has been obtained the repelling for the system. The price dynamics showed a saddle-node bifurcation that determined the equilibrium points of the system and exhibited the U-shaped curve.