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Purpose: The article deals with the features of science and education in the context of the management system, presenting not a traditional management system, but the innovative idea of a migration management model. Design/Methodology/Approach: The study is based on the archive philosophy of M.K. Petrov. Under the conditions of 'big science', its creative potential focusing on innovations in the field of practical applications and in the education system, assigns its generation feature to cybernetic management models. Findings: Authors presents a model of education, facing the issue of management science and education in modern conditions. It analyses the concepts of the 'science of science' and 'society scientification' in the conditions of the modern 'big science'. Practical Implications: The results gives the view on shaping the institute of science in modern times and could be used in managing science and education at all levels. Originality/Value: The study has a unique viewpoint on the framework of science and education, addrssing the very nature of these sociocultural phenomena., peer-reviewed