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The world experience of solving the problems of project management is generally directed to the use of the best practices. But conditions for the improvement and development of organizational structures in management of organizations and enterprises are not always created. In this study, in the context of project management theory, the structure of communication between the main entities of the process: the team, the project and its environment was generalized. The assignment of these components of the project environment to specific discrete states, in which the project system may be, enables to display the system using a Markov chain with three discrete states. The transition probabilities of the Markov chain for the project environment determine its characteristics which vary in discrete time step by step in the form of a certain set of state probabilities. Cognitive features of the model which was built on the basis of a Markov chain allows to assign specific values to the transition probabilities of the system. In this paper, a new approach for determining the values of the transition probabilities is proposed. The transition probabilities are identified with the relative time of resource cost in each of the discrete states. Using the cognitive model that was created by the interaction of the main entities of the project, namely, the team, the project and its environment, the trajectory of the projects development in the case of loyal cooperation and in the case of resistance of the project environment was studied. The received results reflect a strong growth trend of the time resource cost for system interaction with the environment of the project, which eventually will delay the implementation of the project. The obtained results do not contradict the definition of the law of S. D. Bushuev. The structure of the project management in the stage of initiation of the project includes the team, the project and environment of the project. These entities are constantly interacting with each other. The change of the state probabilities of the project fully reflects the progress and impact of the project. This new understanding of the project systems leads us to the development of modern approaches as the basis for new practices in project management.

Development of the model of interaction among the project, team of project and project environment in project system