Nonlinear Optimization of the Chaotic Market Dynamics
In the framework of the theory of dynamical systems a problem of stabilization of chaotic behavior of the good market created by competing firms is considered. The analysis is carried out on the basis of investigations of a quite simple model of two firms which follow the active and asymmetric investment strategies and develop in one and the same market. In the parametric space of the given model areas corresponding to its chaotic behavior are described. It is shown that by means of weak variations of the parameters corresponding to the efficiency of the investment size it is possible to suppress chaos and convert the dynamics of both firms to a periodic regime of functioning. As a result, the situation in the market is stabilized, and both firms increase their profit. It is found that to get this result it is sufficient that only one firm carries the given trade policy. Generalizations of the obtained conclusion in the case of a large number of competitors are presented. The elements of mathematical theory of the stabilization of chaotic dynamical systems are given.