МЕТОД АДАПТИВНОГО КОНТРОЛЯ НЕУСТОЙЧИВОЙ ДИНАМИКИ В ДВУХЭЛЕМЕНТНЫХ СИСТЕМАХ С КОНКУРЕНЦИЕЙ НА ПРИМЕРЕ ДУОПОЛИИ

Research of competition systems’ dynamics is one of the current issues within the framework of systems and processes modeling; in particular, one of such issues is the fact that under certain conditions the systems show undesirable unsteady dynamics which can result in unforeseeable behaviour of the system’s elements. Mathematical models of Cournot-Puu type give an opportunity to analyze such processes, as they take into account real conditions of the competition systems functioning as mentioned above.

Application of the DFC-method with the purpose of stabilizing unsteady behaviour of the systems with competition is expedient along with correlating it to equivalent methods, in particular, to the method of adaptive control – АС-method, basic principle of the latter being the hypothesis that expectations of the system’s elements deviate from "naive" to "adaptive". The optimal value of original characteristic of the system element in a subsequent period which depends on the value of this characteristic in the current period, as well as on the weighted average expected value of the same original characteristic of a competitive element in the current period.

Conducted investigations allow us to draw a conclusion that for the 2-elements systems with competition it is reasonable to apply only one managing function for stabilizing the system chaotic dynamics. Such management restores the system to equilibrium faster as compared to application of two managing functions, i.e. attempts of two elements to stabilize the system simultaneously. For this particular reason application of the adaptive control method, as well as application of DFC-method, to the system structure is also considered to be the method of "individual" control in an unsteady system.

The investigated management systems may be applied not only for stabilizing unsteady dynamics in oligopolistic markets, but also to all systems the elements of which are interrelated and compete for a limited resource.

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