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The mathematical model of the mutual synchronization system with structure having form of the complete graph and composed of n (n ∈ N) oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The step responses matrix of the system is obtained applying the Lambert function method. The transition processes are investigated using obtained step responses of the system.

The use of Lambert function method for analysis of a multidimensional control system with delays and with structure of the complete graph