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**:** 107
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**:** 2024
**:** .., .. // . 107. .: , 2024. .6-27. DOI: https://doi.org/10.25728/ubs.2024.107.1

** :** , , , ,

** (.):** complex system, equilibrium, covering map, coincidence point, elastisity

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** (.):** The paper is dedicated to complex systems analysis, in particular, the question of searching a coincidence point for two mappings. A coincidence point is a point at which the image of one mapping coincides with the one of another mapping at this point. This notion is a generalization of fixed point concept. It can be applied to information processing, artificial intellect and system analysis. Besides, this concept may be applied in economical problems such as resourse management, production volume calculation and price regulation. In this paper coincidence points theory is applied to the question of equilibrium in market system. An equilibrium is a state at which the supply of all goods on the market equals to thier demand. We developed a search algorithm of coincidence point for covering and Lipschitz-continuous mappings. The work of this algorithm is demonstrated on open market model. In this model supply and demand mappings are restored by their price elasticities. Elasticity is a measure of change for one variable under the change of another. We consider partical equilibrium in this model. It is a state at which supply equals demand for some subset of goods, not all of them. Equilibrium is conisedered as a coincidence point of supply and demand mappings. We complement the results with the example of partial equilibrium in the model of two goods.

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