STRANGE ATTRACTORS OF A QUASI-LINEAR MODEL OF THE INTERNATIONAL ECONOMY

Until now, all new "synergetic" concepts and objects in mathematical economics have appeared and studied in systems of nonlinear, but relatively small dimensions (n≤4). The model of the economic system of the 6-th order is considered below. Similar models for the Keynesian economic system have been actively discussed on the Internet since 2010. This paper proposes model parameters for the economies of three states, in which the interaction between economies leads to phase portraits similar to a deterministic chaos like a resonant torus. According to Keynes, the general economic model for one country is a system of two differential equations relating the national income Y and the bank interest rate R. All parameters on the right side are either constant or linearly dependent on Y and R. The introduction of the factor of international trade into isolated systems of states leads to a system of six interrelated equations. Such an extended system consists of three coupled bounded oscillators. As shown by Newhouse, Ruelle, and Takens, perturbation of motion along three-dimensional tori can lead to a strange attractor. Thus, the possibility of the existence of strange attractors was established in the model of international trade. Lorentz showed that the existence of chaotic trajectories in the corresponding models can be established by numerical simulation. Everything previously described refers to nonlinear systems of equations, which are characterized by limit cycles and a strange attractor. But, since our system is linear with constant coefficients, the solution for it can be sought in the form of a linear combination of exponents. If the ratio of periods is irrational, then the movement is chaotic, and it is easy to see that two points at the initial moment of time, lying next to the course of time, can be arbitrarily far away. The following statement becomes true here: If all three autonomous economies are of the oscillatory type, the introduction of international trade could lead to a strange attractor in the unified economy. We have nonperiodic motions in a limited area. This is a strange attractor since it is not a point or a cycle