Abstract
The basic effects and patterns that characterize the Keynesian model of business cycle have been modeled using the system of linear differential equations. The solutions of the system, which describes the interaction of two or three states are found, and stability of this system was investigated. The majority of economic processes proceed in time. Owing to this, corresponding mathematical models are basically dynamic and nonlinear.The similar phenomena were observed in 4 dimentional models for economy of two states. Thus the required combination of parameters has been found, and the hypothesis of chaos as a result of globalization has been proved to be true, even for the elementary models.
Highlights
The majority of economic processes proceed in time
In the given work model parameters of economies of 3 states are offered, at which the collaboration between economies leads to the phase portraits, that are similar to determined chaos of resonant torus type
At the certain combination of constants of this system of the differential equations the pattern shows chaotic behavior at separate intervals of time, and in some cases, phase trajectories leave on torus strange attractor, the objective of the present work is research of a phase portrait of the given system on a randomness
Summary
Owing to this, corresponding mathematical models are basically dynamic and nonlinear. Till all new «synergetic» concepts and objects have appeared and investigated in nonlinear systems with rather small dimension (n ≤ 4). Research of multivariate systems leads to complexities, both theoretical, and computing. The model of economic system of 6-th order is considered below. It is assumed to be linear, it shows the complex behavior, similar to determined chaos, known in nonlinear systems. Similar results for economic system in 2006 were actively discussed on the Internet. In the given work model parameters of economies of 3 states are offered, at which the collaboration between economies leads to the phase portraits, that are similar to determined chaos of resonant torus type. The given system is considered with the purpose of increasing the management efficiency of the union, that is the increase of the income for all or most of the countries from the union
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