In the article, based on data from the Shanghai Ranking (ARWU) 2003-2022, ranking achievements of elite associations of top universities in the USA (AAU), the United Kingdom (Russell Group), Canada (U15 Group), Japan (RU11), China (C9 League), Australia (Group of Eight), Germany (U15), taking into account the political and economic context of their functioning, the factors of the effectiveness of such associations are determined to ensure the leadership of member universities. It has been found that the greatest synergistic effect of association is achieved in small associations or their parts (with the number of up to 10-20 institutions), which include institutions close in terms of ratings, which are characterized by significant (resonant) intragroup interaction and which are provided with strong national support. Activities at the same level of complexity of educational programs and research and development, selective significant cooperation on the principle of "equal to equal" (thus achieving the effect of resonant interaction) serve as a guarantee of successful collective advancement to the top levels of excellence of all participants of the interaction. Otherwise, the formal association either declines or undergoes informal internal stratification (differentiation) into groups more homogeneous in complexity of activity, not all of which can withstand the competitive struggle for leadership and the ability to fully use the advantages of formally open science due to its actual closedness in part complex knowledge for insufficiently capable universities. An alternative to the selective associative union of universities withing the country can be their direct organizational consolidation with systematic state support to transform into powerful university centers, as is done in France, or a strong national policy for the development of flagship universities, as in Switzerland. Scientifically based practical recommendations on the creation of a domestic elite Association of Ukrainian Universities (AUU) and the strategy of their consolidation are formulated in order to overcome the growing global backwardness of higher education of Ukraine, which is especially relevant in the conditions of the specifics of open science and the post-war recovery of the country on an innovative, high-intellectual, and high-tech basis.
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